The under-fire firm, which has seen more than £400 million wiped off its market value since the debacle, repeatedly assured ministers it would "overshoot" its recruitment targets and only admitted it would fail last week, the Home Secretary told MPs.

A further 3,500 troops who were drafted in to close the gap have now been joined by officers from nine police forces after security staff failed to turn up at venues.

Mrs May said G4S have more than 20,000 accredited Olympics staff but the issue was scheduling and "getting staff to the venue security tasks".

Asked why, she said: "I think there are a number of things. The first is about the scheduling problems G4S themselves have had.

"And there will be individuals who are now saying they do not wish to take that work up - that may be for a number of reasons."

But she could not give exact figures for how many guards would now be supplied by G4S, saying only that the "precise balance of the number who will be provided will become clear over the next few days".

Mrs May denied the firm had "deliberately deceived" the Government, telling MPs that the firm made clear that the problems with "workforce supply and scheduling" only emerged "over the last couple of weeks".

She also denied ministers had been told by G4S before last week that the firm would fail to meet its targets.

"G4S repeatedly assured us that they would overshoot their target," Mrs May said.

"G4S only told the Government that they would be unable to meet their contractual arrangements last Wednesday and we took immediate action."

A total of 3,500 troops, many of whom will be billeted at Tobacco Dock near Wapping, east London, were brought in to boost the number of servicemen and women involved in Games security to 17,000 last week.

Hundreds of officers from nine forces have now also been drafted in to fill gaps.

Venue security was being tightened "before the full complement of accredited staff have been assigned", a G4S spokesman said.

"This situation is being rectified over the coming days, which should lead to the withdrawal of police officers from those roles assigned to private security."

The forces involved are Dorset, Surrey, Hertfordshire, Northumbria, South Wales, Strathclyde, West Midlands, Thames Valley and Greater Manchester.

Assistant Commissioner Chris Allison, the national Olympics security co-ordinator, said: "Whilst some of the activity police officers are undertaking was not anticipated, plans were put in place to allow us to do this.

"Forces are making sure they make the best use of their resources locally to do all they can to minimise the impact on local policing."

But West Midlands Police Federation chairman Ian Edwards said it was "chaos, absolute chaos".

The force has had to provide 150 officers per day to cover a hotel in Warwickshire where footballers are staying, he said.

"The worst-case scenario is that we end up having to find another 200 officers for the security at the City of Coventry stadium, and we've yet to find out what the shortfall is in Birmingham. It's chaos, absolute chaos.

"You shouldn't lose your local police officer because of the Olympics. Communities are suffering because a private company has failed to deliver on a contract."

Clive Chamberlain, chairman of Dorset Police Federation, added G4S staff were simply not turning up.

He said: "On a daily basis it's a lottery as to how many staff are going to turn up. The best they've managed is 15% not turning up, and on the worst occasions they have been 59% down. It's a fiasco, it's an absolute debacle.

"My biggest fear is that G4S are now panic-recruiting people to get as many people as they can into the organisation. Two weeks before the Games, we are going to have hundreds or thousands of people that are going to need to be properly vetted, that comes down to the police.

"What proper training will they have had before they start? It's very, very worrying."

Assistant chief constable Terry Sweeney, of Greater Manchester Police, said officers were called in to help protect athletes at the main Olympic team hotel in Worsley yesterday after the force became aware of a shortfall on Saturday.

Shadow home secretary Yvette Cooper said: "It is incomprehensible that with 11 days to go the Home Secretary still doesn't know how many staff G4S are likely to provide.

"We all want the G4S shambles sorted out swiftly now. But if even more troops and police are going to be needed they need to know fast so they can prepare."

A confidential report by HM Inspectorate of Constabulary (HMIC) warned about concerns over security 10 months ago, leading Games organisers Locog to increase the number of security guards to be supplied by G4S from 2,000 to 10,400 while the value of the contract more than trebled from £86 million to £284 million.

G4S chief executive Nick Buckles, who is due before the Commons Home Affairs Committee tomorrow, has admitted he may be forced to quit his £830,000-a-year job in the wake of the debacle, which is expected to leave the firm with a loss of up to £50 million on the high-profile contract.

PA