London 2012 chairman Lord Coe
London 2012 chairman Lord Coe has promised a "safe and secure Games" despite the security guards fiasco.
"We have got the numbers, courtesy of the military and our police services," he told BBC Radio 4's Today programme.
An extra 3,500 troops were drafted in last week after security firm G4S admitted a shortage of staff, and a further 1,200 troops are on standby.
Lord Coe added that people involved in the Games were " overwhelmingly very positive about what we are doing".
The head of security and counter-terrorism at the Home Office, Charles Farr, has told the BBC that plugging the G4S with military personnel meant that in some respects there was an even stronger workforce now involved in the security operation.
Lord Coe said: "This is not an issue that has remotely compromised security. This was actually about the supply and the mix, it's never been about the numbers.
"We have got the numbers, courtesy of the military and our police services, we have got the numbers to make sure that this is a safe and secure Games."
Farr said he had first learned of recruitment problems at G4S in late June, from when he and ministers monitored the situation closely and put contingency plans in place.
But it was not until July 11 that G4S had confirmed it could not meet its commitments, he said.
This was, Farr said, after he asked for a guarantee at a meeting of the government's Olympic Security board.
On Thursday, Immigration Minister Damian Green told BBC Two's Newsnight: "It was only on July 11 that G4S said, 'No, we're not going to get the numbers we wanted,' at which point the plans that had sensibly been put in place in advance were actually put into action."
G4S released a statement saying it was making "good progress" and there were daily increases in the number of people working at Olympic venues who had completed training and accreditation.
Lord Coe said: "It is very important to keep this in perspective. There are 4,000 people from G4S who have been working very successfully currently on the park and have been working successfully for many years on this."
He went on to stress the scale of the task of hosting an Olympics, which effectively involved staging "in 19 days, in this city, 26 simultaneous world championships".
"No city is challenged in the way a city is challenged when it delivers an Olympic Games."
But he added: "I'm talking to people who think they have come to a Games that has delivered in the areas that they need in a way that no Games has delivered before.
"I spent time in the village yesterday talking to athletes that were complimenting us about the Athletes' Village we have presented.
"One Australian broadcaster came up to me: 'I've been to four Games, this is by a distance the best broadcast facility.'
"Everywhere we go, the reality of it is people are overwhelmingly very positive about what we are doing."