George Osborne hinted today that Britain could contribute more to the IMF after a rescue package was agreed for the eurozone.
But the Chancellor sought to reassure Tory backbenchers that UK money would not be earmarked to bail out the struggling single currency area.
Markets around the world have surged after hours of tense negotiation in Brussels finally produced a deal designed to cool the crisis.
Banks have agreed to take a 50% write-off on their Greek debt holdings, and the European Financial Stability Facility (EFSF) is to be leveraged to 1 trillion euro (£880 billion).
Billions will also be pumped into vulnerable banks to protect them from failure.
The measures did not go as far as many financial experts had been demanding over recent months.
But updating MPs on the developments, Mr Osborne said the eurozone now appeared to be on the "right road".
"Our view is that last night very good progress has been made towards solving the immediate crisis, very good progress on all fronts," he said.
"But much detail remains unresolved and having put pressure on the eurozone to get this far, we have to keep up the pressure to get the details completed.
"They have started down the right road and now they have to finish the job."
He insisted that Britain will not contribute money to the EFSF bailout fund - but did concede that extra money could go to the IMF.
"Supporting countries that cannot support themselves is what the IMF exists to do and there may well be a case for further increasing the resources of the IMF to keep pace with the size of the global economy," he said.
"Britain, as a founding and permanent member of its governing board, stands ready to consider the case for further resources and contribute with other countries if necessary."
But he stressed: "We are only prepared to see an increase in the resources that the IMF makes available to all countries of the world. We would not be prepared to see IMF resources reserved only for use by the eurozone."
Speaking en route to a Commonwealth meeting in Australia, David Cameron also welcomed the deal.
"Last night they put in place the key elements needed to tackle the urgent crisis in the eurozone: strengthening the banks; building a firewall; dealing more comprehensively with Greek debts," he said.
"They made very good progress. They need to keep up the momentum and work urgently to fill in the remaining detail."
However, Tory backbenchers are already signalling their willingness to oppose any effort to boost Britain's contribution to the IMF.
Basildon MP John Baron and Amber Valley MP Nigel Mills were among those who challenged Mr Osborne on the issue in the Commons.
Mr Mills expressed concern that "the IMF does not end up supporting a currency if a country chooses not to take the right action".
Outside the chamber, Shipley MP Philip Davies accused Mr Osborne of "dancing on the head of a pin" by suggesting funds given to the international body would not end up bolstering eurozone countries.
"The last drop of goodwill has been used up for bailing out countries in the eurozone through one mechanism or another," he said.
"There is no point trying to bamboozle us with methods. It is not acceptable to bail it out through the back door."
Mr Davies repeated his threat that a rebellion over IMF funding could make this week's damaging EU referendum revolt look like a "child's tea party".
"They have used up the last drops of goodwill," he added.
Under the terms of the Brussels deal, European banks will have to increase cash buffers designed to protect against future crises - known as Tier 1 capital ratios - to 9% until next June.
Banks will be expected to try first to use private sources of capital to raise the 108 billion euro (£94 billion) needed to beef up these protective cushions but the state will step in if this is not possible.
EU leaders said they would finalise Greece's second bailout package by the end of the year, which will include a higher private sector involvement.
The private sector - predominantly financial institutions such as banks - has been asked to write off 50% of its Greek debt.
The eurozone will contribute an additional 100 billion euro bailout to this write-down in a move to lower Greek debt to 120% of GDP by 2020.
The FTSE 100 closed 3% higher as investors drew confidence from the political agreement - even though many had been calling for more debt to be written off and a larger bailout fund.
In France, the CAC index rose more than 6%, while the Dax in Germany increased by more than 5%.
Banks led the rally, with Barclays and Royal Bank of Scotland rising 18% and 10% respectively.
The euro also strengthened against both the dollar and the pound.