The Home Secretary admitted the Government and organisers Locog knew there were problems and that the firm, the world's second largest private sector employer, could fail to meet its contract as early as June 27.
It comes after the company's under-pressure chief executive Nick Buckles told MPs that he did not tell organiser Locog about the problems until a week later and Mrs May told the Commons the "absolute gap in numbers" was not known until July 11.
The revelation came as a further 1,200 troops were put on standby to provide Olympics security on Thursday night as the fallout from the shambles continued. But the Government said the numbers of staff provided by the company were rising, and there was currently no need to deploy more military personnel.
Shadow home secretary Yvette Cooper said: "The Home Secretary was asked repeatedly when she and the Home Office were warned about problems at G4S, and she repeatedly gave everyone the impression they had only known since July 11. Why has Theresa May waited until now to admit the Home Office in fact were warned two weeks earlier? She needs to explain urgently how she justifies having given Parliament and the public such a selective account, and why the Home Office were so slow to respond."
The details were revealed by Mrs May in a letter to the Commons Home Affairs Select Committee. Labour MP Keith Vaz, the committee's chairman, said: "The Home Secretary told the House that she only became aware of a shortfall on the 11th July. However, this letter clearly states they were warned of a possible shortfall in guards on the 27th June at the Olympic Security Board, two weeks before."
He called for any updates on the figures contained in monthly internal assurance reports to be released and for an explanation as to "why they did not ring alarm bells sooner". But a Home Office spokesman said: "Mr Buckles' evidence to the Home Affairs Select Committee this week confirmed what the Home Secretary told the House of Commons: G4S did not tell ministers that they would be unable to deliver their contractual obligations until July 11."
While 750 troops were put on 24 hours' notice last month, the extra 3,500 servicemen and women who will plug the gap left by G4S were not called in until two weeks' later after the company confirmed its "absolute" shortfall.
Mrs May admitted that permission to put a small part of the military contingency force on 24 hours notice was sought as early as June 28, with the force being mobilised "several days later". This was increased to 725 troops by July 9 and plans to put even more troops on standby got under way on July 6, she added. "But at this stage, of course, G4S were still confident that they would deliver the required numbers," Mrs May said. "However, as we now know, this is no longer the case. On July 11 G4S told the Olympic Security Board for the first time that they were no longer confident of reaching their workforce targets."
Immigration Minister Damian Green said G4S first admitted recruiting problems in June, but the difficulties only "crystallised" weeks later. He told BBC Two's Newsnight: "What happened on June 27 was that G4S said there might be a problem, they were behind (in the recruitment) but they were confident that they would have the numbers they promised. 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."