Media playback is unsupported on your device Media caption David Cameron: "I hope people will see all the things they love about Britain's past and our institutions and culture"

The London 2012 Olympics will show the world "beyond doubt that Britain can deliver", the prime minister has said.

"Look at what we're capable of... even at a difficult economic time," he said, after US presidential candidate Mitt Romney raised doubts about the Games.

The Olympic torch visited No 10, where it was greeted by David Cameron, and it is now on its way to Buckingham Palace.

Meanwhile, the BBC's James Pearce says it looks likely that the opening ceremony on Friday will not sell out.

Our Olympics correspondent says spare seats are likely to be filled by troops or children, but a decision will be taken on the day of the ceremony.

Games organisers Locog said there were still tickets available for the event, priced at £2,012 and £1,600 each.

Organisers also posted a message on the London 2012 ticketing website to say that seats bought after 17 July will have a restricted view.

During the news conference at the Olympic Park, alongside London 2012 chairman Sebastian Coe, Mr Cameron told reporters: "This is a great moment for us. Let's seize it."

He said security was his main concern ahead of the Games.

"As prime minister, I feel that is an area I should take personal responsibility for," he said.

"The biggest concern has always got to be a safe and secure Games - that matters more than anything else."

In other news:

The men's football is now under way, with eight matches taking place on Thursday, including Britain v Senegal at 20:00 BST (19:00 GMT)

Long queues outside St James's Park in Newcastle meant some football fans missed the start of Mexico v South Korea

The PM met David Beckham at Downing Street to discuss how to tackle world hunger. It came ahead of a "hunger summit" on the final day of the Games, Sunday 12 August

A planned strike by East Midlands Trains (EMT) during the Games has been called off after a pensions dispute was settled

Locog has apologised after an official football programme listed Welsh footballer Joe Allen as English. It said the error would be corrected for Team GB's next match

A unanimous decision has been made over who will light the Olympic Stadium's cauldron, Locog says, but it will be kept secret until the ceremony

A global investment conference in London has kicked off a series of business summits intended to showcase the UK and attract investment during the Games

A new record for arrivals at Heathrow is expected to be set on Thursday, with up to 125,000 incoming passengers

On Wednesday night, Games organisers apologised to North Korean athletes whose images were shown next to the South Korean flag.

Mr Cameron earlier played down the flag blunder, which happened on the first day of sporting action, and delayed the women's football match between North Korea and Colombia at Glasgow's Hampden Park by about an hour.

Media playback is unsupported on your device Media caption Organisers have released a short clip from the dress rehearsal of the Olympic Games opening ceremony

"This was an honest mistake, honestly made," Mr Cameron said.

"An apology has been made and I'm sure every step will be taken to make sure these things don't happen again."

The prime minister called the eve of the Games "a truly momentous day for our country".

"Seven years of waiting, planning, building, dreaming, are almost over - tomorrow, the curtain comes up, the spectators arrive, and the Olympic and Paralympic Games 2012 can officially begin."

'Coming together'

Mr Cameron earlier met the Republican candidate for the US presidency, Mitt Romney, during his campaigning and fundraising visit to London.

The meeting came after Mr Romney expressed concerns about "disconcerting" signs of a lack of readiness for the Games.

"The stories about the private security firm not having enough people, the supposed strike of the immigration and customs officials - that obviously is not something which is encouraging," Mr Romney told a US television station.

It was "hard to know just how well it will turn out", said Mr Romney, who managed the Winter Olympics in Salt Lake City in 2002.

Mr Cameron responded: "Of course, this is a time of some economic difficulty for the UK. Everybody knows that.

Media playback is unsupported on your device Media caption Mitt Romney: "I'm excited about the opening of the Olympics"

"But look at what we're capable of achieving as a nation, even at a difficult economic time."

He added: "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.

"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."

Mr Romney, who also met Labour leader Ed Miliband, later said outside Number 10: "I expect the Games to be highly successful."