Private security firm G4S told the Home Office it would be able to resolve its problems supplying Olympic guards last month, Theresa May said.
On a tour of the Olympic Park's security centre, the Home Secretary said G4S, the world's second largest private sector employer, told officials that any problems were temporary and would be resolved.
She denied being selective in what she told MPs, insisting that the gap in the numbers only became clear on July 11, not two weeks earlier when the firm first reported problems.
"In early July it was clear that there were some initial problems which G4S said they would resolve," Mrs May said. "And crucially it was not until July 11 that G4S finally said, 'Actually we can't resolve those initial problems, we won't be able to provide the personnel'."
She went on: "I haven't been at all selective. What I've been is absolutely clear with the House of Commons and others about how these things developed."
Asked what the Home Office was told at a meeting with G4S and Olympic organisers Locog on June 27, Mrs May said: "What happened was there were some early signs of a problem with rostering staff for G4S.
"It was clear that G4S felt they were capable of dealing with that, that it would be resolved, and it was on July 11 as the chief executive of G4S told Parliament, the home affairs select committee, that G4S said 'Actually, we now believe we cannot produce the staff we were contracted to produce'."
Mrs May said the issues with G4S supplying enough guards initially looked like "teething problems". She said: "They were consistently telling us, up until July 11, that they could produce the number of people required for the Olympic Games. Asked if G4S should have acted sooner, Mrs May said they believed they had identified a "temporary problem which was capable of resolution".
Labour leader Ed Miliband backed servicemen and women to fill the gap left by G4S's failure to fulfil its contract. Speaking on a visit to Corby in the East Midlands, he said: "I think we are going to be ready for the Olympics. The job that the troops and police are doing in stepping in where G4S failed is, frankly, brilliant.
"We've got to get behind them and I'm sure, well I hope, enough is being done that we have a safe and successful Games. I trust that is going to happen because we now know that we've got the troops and the police stepping in."