David Cameron has said every effort will be made to ensure mistakes such as last night's Olympic flag mix-up never happen again.
The Prime Minister said the error in which the South Korean flag was wrongly shown instead of sworn enemy North Korea's at a football game was "an honest mistake" for which an apology has been issued.
"Every effort will be taken to make sure this won't happen again," Mr Cameron said.
The North Korean women's team staged a protest ahead of their match with Colombia after the South Korean flag was wrongly shown on a big screen at Glasgow's Hampden Park stadium.
As a consequence, the players walked off the pitch and delayed the match by an hour.
"It was unfortunate and should not have happened," Mr Cameron said.
Speaking on a visit to the Olympic Park, Mr Cameron said: "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.
"We shouldn't over-inflate this episode. It was unfortunate, it shouldn't have happened and I think we can leave it at that."
On security, he said that from chairing the Government's Cobra meetings he knew "just how much thought has gone into providing the physical security for people here in the park, and in the country as a whole.
"You can never provide a 100% guarantee but what I've seen and what I've helped to co-ordinate is, I think, a fully joined-up effort which involves one of the best armed services anywhere in the world, very very professional people looking at every eventuality, a very efficient police service and also a lot of security here on the ground at the Games."
Asked about US Republican presidential candidate Mitt Romney's comments questioning Britain's readiness to host the Olympics, Mr Cameron said: "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.
"Look behind me at this extraordinary Olympic Park, built from nothing in seven years.
"Let me pay tribute by the way to the government that came before mine and the one before that - all played a role in this.
"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."
People have to be prepared for some difficulties when one of the busiest cities in the world is hosting the Olympics, the Prime Minister said.
"This is an extraordinary few weeks for London," Mr Cameron said.
"We can't say to people that life is going to be completely as normal, it isn't.
"This is an extraordinary few weeks for our city, for our country, and I think people have to be prepared for some difficulties as a result of that."
He went on: "We are holding an Olympic Games in one of the busiest, most active, bustling cities anywhere in the world.
"Of course it's easier if you hold an Olympic Games in the middle of nowhere.
"Inevitably you're going to have challenges".
There were "immense challenges" at Heathrow Airport, he added, but the reports were that people were coming through there "very, very quickly".
"Obviously there are transport challenges in London, but I think the flexibility that has been shown about the Games Lanes, only restricting them to the Games traffic when it's necessary - of course that makes it more complicated, but I think that's showing real flexibility and is right."
Mr Cameron added that he travelled to the Olympic Park on the Jubilee line this morning.
Referring to the public transport system, Mr Cameron added: "Of course it's going to be challenging, but so far I would argue it's held up well."
He added: "There are always lessons to learn from your country's preparations.
"Clearly, the difficult issue of the last two weeks of getting the security right - we've had to act and act quickly to make sure that everything is working properly."
Mr Cameron also said he took personal responsibility for the security 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."
He went on: "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.
"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."
He added: "We've got great hopes for what Team GB are going to do, I think its spirit is amazing. It's great that we have so many medal hopes across so many different sporting endeavours."
On the security risk, Mr Cameron said: "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."
Earlier, ahead of meetings with Mr Cameron, Nick Clegg and Ed Miliband, Mr Romney told US television there were "disconcerting" signs.
Mr Romney told NBC News: "It's hard to know just how well it will turn out.
"There are a few things that were disconcerting.
"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."
Barack Obama's Republican challenger is expected to stress his commitment to the "special relationship" as he uses the trip to raise funds and canvass support among London's large American community.
But in the interview 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.
Asked about Olympic security issues and the error over the North Korean team flag as he met Labour leader Ed Miliband in Westminster today, Mr Romney replied: "It is impossible for absolutely no mistakes to occur.
"Of course there will be errors from time to time, but those are all overshadowed by the extraordinary demonstrations of courage, character and determination by the athletes.
"The Games are, after all, about the athletes, the volunteers and the people of the community who come together to celebrate those athletes.
"As soon as the Games begin, we all forget the organisers and focus on the athletes."