The Prime Minister said he would do "whatever it takes to keep Britain safe from the storm", but made clear that the UK could not be immune from the consequences of a collapse of the euro.
He insisted he would not ditch the coalition Government's deficit-reduction strategy in the face of demands from Labour - echoed by new French president Francois Hollande - for a shift in focus from austerity to growth.
Britain should be "resolute" as it faces the potential storms from the eurozone, but also "confident" that it can get through to a brighter future if it stands firm and resists the "dangerous voices calling on us to retreat", he said.
In his starkest warning yet of the dangers created by the debt crisis in Greece, the Prime Minister used a high-profile speech on the economy to say that Britain is going through "perilous economic times".
Citing Bank of England governor Sir Mervyn King, who yesterday warned that the eurozone seemed to be "tearing itself apart", Mr Cameron told an audience of business leaders in Manchester: "Turn on the TV news and you see the return of a crisis that never really went away. Greece on the brink; the survival of the euro in question.
"Faced with this, I have a clear task: to keep Britain safe. Not to take the easy course, but the right course. Not to dodge responsibility for dealing with a debt crisis, but to lead our country through this to better times.
"My message today is that it can be done. We are well on the way in this journey."
In a message directed at Germany - which yesterday registered strong growth while other eurozone countries saw their economies shrink - Mr Cameron said the "remorseless logic" of monetary union meant that successful economies must be prepared to do more to shore up weaker states on the periphery.
While high-deficit countries like Greece need to take steps to get their budgets in order, "it is becoming increasingly clear that they are less likely to be able to sustain that necessary adjustment economically or politically unless the core of the eurozone, including through the European Central Bank, does more to support demand and share the burden of adjustment", he said.
The eurozone needs to put in place long-term governance arrangements - such as eurobonds - which will deliver collective support and put an end to speculation about the future of the single currency.
And Europe needs to implement structural reforms to address its overall low productivity and lack of economic dynamism, he said.
"The eurozone is at a crossroads," said Mr Cameron. "It either has to make-up or it is looking at a potential break-up.
"Either Europe has a committed, stable, successful eurozone with an effective firewall, well capitalised and regulated banks, a system of fiscal burden sharing, and supportive monetary policy across the eurozone, or we are in uncharted territory which carries huge risks for everybody.
"As I have consistently said, it is in Britain's interest for the eurozone to sort out its problems.
"But be in no doubt: whichever path is chosen, I am prepared to do whatever is necessary to protect this country and secure our economy and financial system."
Despite the market turmoil across Europe sparked by the failure to agree a new government in Greece, Mr Cameron insisted there was reason for optimism that the UK is on the path of recovery.
He hailed today's announcement of a £125 million investment by General Motors in its Vauxhall plant in Ellesmere Port, which he said was part of a wider revival in the British car industry which had seen the balance of trade in cars turn positive for the first time since 1976.
"Despite headwinds from the eurozone, we are on track," said Mr Cameron. "It is a long-term project. It is painstaking work. But the tough decisions we have taken on deficit reduction really are beginning to yield real results. And there can be no deviation from this."
He dismissed Labour's call for a relaxation in the Government's austerity programme in order to stimulate growth as "a cop-out", which would drive up interest rates and put recovery at risk.
"Deficit reduction and growth are not alternatives. Delivering the first is vital in securing the second," he said.
And he insisted: "We are moving in the right direction - not rushing the task, but judging it carefully. And that is why we must resist dangerous voices calling on us to retreat.
"Yes, we are doing everything we can to return this country to strong, stable economic growth. But no, we will not do that by returning to the something-for-nothing economics that got us into this mess.
"We cannot blow the budget on more spending and more debt. It would squander all the progress we've made in these last two, tough years.
"It would mean tough decisions lasting even longer. It would risk our future. It's not an alternative policy, it's a cop-out."
Britain's "responsible fiscal policy" of cutting spending and increasing taxes allowed the Bank of England to pursue an active monetary policy to support the wider economy, said Mr Cameron.
And he said the Government was also pursuing a "radical programme of micro-economic reform" to boost competitiveness, including low corporate taxes, loan guarantees, streamlined planning rules, enterprise zones, labour market reforms and support for apprenticeships, as well as long-term action to invest in infrastructure, reform welfare and improve schools.
"As we get through crisis, I believe we can look ahead with confidence," said the Prime Minister.
"I cannot predict how this crisis will end for others. And I cannot pretend that Britain will be immune from the consequences, either. But this I can promise: that we know what needs to be done and we are doing it.
"Get the deficit under control, get the foundations for recovery in place, defend the long-term interests of our country and hold our course.
"As Prime Minister, I will do whatever it takes to keep Britain safe from the storm."
Mr Cameron will have a video conference call with French President Francois Hollande, German Chancellor Angela Merkel and Italian Premier Mario Monti this afternoon.
They will be joined by the president of the European Council, Herman Rompuy, who suggested the discussion ahead of the G8 meeting starting tomorrow, and EU commission president Jose Manual Barroso.
It will be the second time Mr Cameron has spoken to Mr Hollande since his election victory.
Shadow chancellor Ed Balls said Mr Cameron was "deeply complacent" if he
believed his Government's policies had put Britain on the right course.
Mr Balls said: "Plan A has failed in Britain, but it is also now failing across the eurozone. David Cameron must recognise the austerity policies which are failing in Europe are the very same policies that have failed in Britain and which the British Government has been urging eurozone countries to stick with.
"Our Prime Minister should be pushing for a positive resolution to the crisis and a change of course in Europe, on austerity and on the role of the European Central Bank.
"And instead of using the eurozone crisis as an excuse for Britain's problems, David Cameron must wake up to the fact that our economy has not grown for over a year and a half on his watch. When countries like France and Germany have avoided recession, despite the eurozone's problems, it's clear Britain's double-dip recession was made in Downing Street."
Meanwhile the secretary general of the Organisation of Economic Co-operation and Development, Angel Gurria, issued a call for industrialised countries to take action to create jobs as a means of sustaining recovery.
In a joint statement with International Labour Organisation director-general Juan Somavia following an employment summit in Mexico, Mr Gurria called on governments of the G20 major economies - including the UK - to "put a greater, renewed emphasis on employment policies that
will help economies accelerate and sustain the recovery, achieve higher
levels of decent work and get out of the debt trap".
They added: "It is critical that the G20 agenda delivers on economic growth and on jobs.
"The short and medium-term challenges faced by G20 countries call
for new measures. We encourage the G20 to consider in particular the promotion of investment in infrastructure, ensuring continued access of SMEs to bank credit, freeing up product markets in ways that promote job
creation, expanding the coverage of basic social protection, and ensuring all youth achieve a smooth transition from school to work."
Business Secretary Vince Cable cautioned against "panicking" and said the UK would be at economic risk only if the crisis spreads beyond Greece.
Mr Cable told BBC Radio 4's Today programme: "There clearly are risks to the UK. Greece itself is a small country, it's only 2% of the European economy. The risks arise if the crisis were spread to other weaker countries in southern Europe, but there is no reason why that should happen.
"They are in the process of creating firewalls to prevent the financial crisis spreading and we hope that they do."
He added: "I don't think there's any reason whatever why in the UK we should be panicking or taking an excessively negative view."
Mr Cameron acknowledged that some eurozone countries may not take kindly
to being lectured on their economic policies by a country from outside the single currency area.
"I realise that countries inside the eurozone may not relish advice from countries outside it - especially from countries, such as Britain, with debts and difficulties of their own," he said. "But this affects us
too ... it's only right that we set out our views."
Conservative deputy chairman Michael Fallon said the PM was right to sound a warning.
Mr Fallon told BBC News: "The Prime Minister has to warn - and I think he was right to do so - that Europe really is at a crossroads now.
"If they don't sort out the mess in Greece and put a sufficient firewall around Greece to stop the contagion spreading across the Mediterranean and if they don't focus on growth, then that is going to drag everybody down.
"The Prime Minister is perfectly entitled to point that out and he will be having meetings with the German chancellor and the new French
president to make his views known."
PA
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