Theresa May said G4S and Locog met at the Home Office on June 27 and said they were "experiencing scheduling problems" which could see a shortfall of "significantly less than 1,000" guards.
But the firm was "unable to specify the size of the shortfall" and only said they were no longer confident of reaching their workforce targets on July 11.
The details came in a letter from Mrs May to Labour MP Keith Vaz, chairman of the Commons Home Affairs Select Committee, and as another 1,200 troops were put on standby to provide Olympics security tonight as the fallout from the G4S chaos continued.
But Culture Secretary Jeremy Hunt said the numbers of staff provided by the company were rising, and there was currently no need to deploy more military personnel.
Mrs May wrote: "On June 27 G4S and Locog attended an Olympics Security Board meeting at the Home Office and said they were experiencing scheduling problems.
"They warned of a possible temporary shortfall in G4S deployed number from July 1.
"G4S were unable to specify the size of the shortfall and could say only that it would be 'significantly less than 1,000'.
"G4S stated that the shortfall was mainly due to the failure to take account of the fact that large parts of their workforce would be unable to begin work before July 27."
Mrs May went on: "Locog and G4S were pressed to clarify the shortfall and factors which had created it urgently.
"The meeting considered a possible short-term and temporary call on the military contingency force (MCF) which had been created for Olympics purposes."
Mrs May admitted that permission to put "a small part of the MCF" 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, she added.
Plans to put even more troops on standby were under way on July 6.
"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."
The contingency plans were activated and 3,500 servicemen and women were brought in to boost the number of military personnel involved in Games security to 17,000.
Mr Vaz 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 went on: "We now know there must have been serious concerns as some 725 military personnel were deployed and contingencies started to be made before the 11th July.
"I am most surprised that G4S have found themselves in this position considering that four separate reports into Olympics security were conducted in the last 12 months.
"We must know the figures that these monthly internal assurance reports revealed and why they did not ring alarm bells sooner."
Earlier, Culture Secretary Jeremy Hunt said: "As we have said, we must prepare for every contingency.
"We are therefore putting an additional 1,200 troops on standby, reducing their notice to move from seven days to 48 hours. They will remain in their current locations but can be called on if we need them during the coming weeks.
"We hope that will not be necessary but this is a sensible precaution."
He went on: "Ministers agreed today that there is no current need to deploy any additional troops.
"G4S numbers are rising and we are seeing an improvement in the company's performance, which is to be welcomed.
"There will be other challenges over the coming weeks, but we are confident that we are on track to stage a great Games."
Asked by Mr Vaz in the Commons last Thursday for the "exact date that ministers found out about the security shortfall", Mrs May said: "We were receiving reassurances from G4S until very recently, and the absolute gap in numbers was crystallised finally only yesterday.
"Because we have been monitoring the situation, we had had discussions with the MoD about whether troops would be available for the contingency, should the circumstances have arisen in which that was necessary, and that is why yesterday we were able to take that decision, having prudently had those discussions and made those contingency arrangements.
"As I said in my response to this urgent question, we have been monitoring. Monitoring has been taking place throughout the contract process and we have obviously been testing and challenging the assurances that we have been receiving from G4S."
Today, an MoD spokesman said: "We can confirm that we are putting a further 1,200 troops on standby as a sensible and prudent measure to provide resilience to the Olympic securityeffort.
"This is in addition to the military contributions already announced and will help re-build our contingency.
"The Government has judged that there is no current need to deploy these additional personnel who will only be called on to deploy if needed - but safety and security for the Games is the highest priority and so we must prepare for every contingency.
"As we have previously said, no member of the of the armed forces will lose leave or be left out of pocket due to Olympics duties."
It comes after a humiliating appearance by G4S chief executive Nick Buckles before Mr Vaz's committee on Tuesday.
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.
"Before that date, Home Office ministers and officials were aware of some challenges for G4S in delivering those obligations, particularly the rostering of staff.
"However, until July 11, G4S continued to tell the Home Secretary, ministers and officials that they would still deliver their Games time obligations.
"When, on July 11, G4S said for the first time that they would not deliver, ministers acted immediately to resolve the problem."
Mr Buckles admitted there would be financial consequences from the company's failure to recruit enough staff.
But he dismissed the idea of giving up the firm's £57 million management fee.
Speaking during a visit to Afghanistan, Prime Minister David Cameron said: "If a company doesn't fulfil its contracts, then that company should be gone after for that money and that's exactly what's going to happen in the case of G4S.
"I couldn't be clearer - we will do what is necessary and contracts that aren't fulfilled will have consequences, including pretty tough financial consequences.
"I think G4S, in apologising for their performance, have already made clear that they realise that fact."
Earlier, Ed Miliband called for G4S to be blocked from getting new Government contracts in the wake of the Olympics security shambles.
The Labour leader said no more deals should be signed until a review had been carried out to ensure the firm was fit to provide services.
And he insisted it "beggared belief" that G4S was trying to cling on to the multi-million pound management fee for Olympics security.
But he refused to call for Mr Buckles' immediate resignation, suggesting the Games needed stability.
"Clearly the company will have serious questions to answer about new leadership (after) the Olympic Games," Mr Miliband said.
Meanwhile, an influential group of MPs has insisted the security staff chaos was "predictable".
The Public Accounts Committee (PAC) said the problems had undermined confidence in Games organisers and demanded that the Home Office "get a grip" on the situation.
PA
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