David Cameron dismissed concerns that Britons might not be behind the Olympics today, saying the Games were a great moment for the UK to come together.
The Prime Minister said the enthusiasm which had greeted the torch relay over the last two months showed they were not a London Games, not an England Games, but a United Kingdom Games.
His comments came after US presidential hopeful Mitt Romney said there were "disconcerting" signs ahead of the Olympics and questioned whether the British people were behind the event.
Mr Cameron said: "Let's put our best foot forward, we're an amazing country with fantastic things to offer. This is a great moment for us, let's seize it."
Speaking in front of the Olympic Stadium where tomorrow's opening ceremony promises to be the greatest show on earth, Mr Cameron said: "The worries we all have are the great hopes and fears.
"Our fingers are crossed for everything from the events to the weather to the transport infrastructure and everything else.
"But, from where I stand, I think we're set for a really remarkable few weeks for Britain, when we welcome the world, say this is a great country to come, enjoy the Olympics, but also think of all the other things we've got to offer."
He went on: "Of course, this is a time of some economic difficulty for the UK, everybody knows that.
"But look at what we're capable of achieving as a nation, even at a difficult economic time.
"In terms of the country coming together, I think the torch relay really demonstrates that this is not a London Games, this is not an England Games, this is a United Kingdom Games."
The Olympic flame will pass through the grounds of Buckingham Palace later, witnessed by the Duke and Duchess of Cambridge, as well as Trafalgar Square, Downing Street and the West End a day before its 70-day, 8,000-mile journey comes to a close.
Mr Cameron went on: "I think we'll show the whole world not just that we've come together as a United Kingdom, but also we're extremely good at welcoming people from across the world."
He said he had "great hopes" for Team GB, saying its spirit was amazing with "so many medal hopes across so many different sporting endeavours".
The Prime Minister admitted that last night's flag mix-up which angered the North Korean women's football team was unfortunate and should not have happened, but warned that the episode should not be over-inflated.
"This was an honest mistake, honestly made, an apology has been made and I'm sure every step will be taken to make sure these things don't happen again," he said.
The North Korean women's team staged a protest ahead of their match with Colombia after the flag of their sworn enemy South Korea was wrongly shown on a big screen at Glasgow's Hampden Park stadium.
The players walked off the pitch and delayed the match by an hour.
Taking personal responsibility for the security of the Games, Mr Cameron admitted there were lessons to be learned from the shambles which saw private firm G4S fail to provide enough guards and the number of troops boosted to 18,200.
But he insisted the military, police, intelligence services and security guards were all working together.
"Anything that you put on inevitably has the danger of attracting bad people who want to do bad things, and Britain gets targeted by those people, as other countries do as well," he said.
"As Prime Minister, I feel that is an area I should take personal responsibility for.
"The biggest concern has always got to be a safe and secure Games - that matters more than anything else."
Earlier, Barack Obama's Republican challenger Mr Romney expressed doubts over the Games on US television.
"It's hard to know just how well it will turn out," he told NBC News.
He also called into question whether the British people were behind the Games.
"Do they come together and celebrate the Olympic moment? And that's something which we only find out once the Games actually begin," he said.
Elsewhere, the travel problems that look set to plague the Games continued with the Heathrow Express rail service temporarily shutting down, causing travel problems for passengers flying into the capital on the eve of the Olympics.
But Mr Cameron, who travelled to the Olympic Park on the Jubilee line, said that overall the public transport system was holding up well.
People have to be prepared for some difficulties when one of the busiest cities in the world is hosting the Olympics, he said.
Efforts to keep the highlights of tomorrow's £27 million opening extravaganza secret were also stepped up, with footage of last night's dress rehearsal removed from YouTube.
Some bookmakers have closed betting on Sir Roger Bannister, the first man to run a mile in less than four minutes, being chosen to light the Olympic Flame at the opening ceremony.
Mr Cameron said that after seeing some presentations on the ceremony he believed the audience would experience some "spine-tingling" moments.
The ceremony has yet to sell out, with tickets still available for more than £1,500.
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