Security firm G4S has said it stands to lose up to £50m after it announced it was unable to provide enough security guards for the London Olympics.
G4S said it was "deeply disappointed" and accepted responsibility for the costs of extra military personnel.
The Commons Public Accounts Committee has summoned G4S, two government departments and 2012 organiser Locog to answer questions in September.
MPs want to know why G4S was unable to hire enough staff.
G4S has issued a statement saying it deeply regretted that it would not be able to fulfil the contract.
It said it had encountered serious difficulties in processing applicants and stood to lose between £35m and £50m on the contract, which is worth £300m.
G4S said it did not underestimate the impact on the military personnel and their families and wanted to express its appreciation to them.
Chief executive Nick Buckles said: "We are deeply disappointed that we have not been able to fully deliver against our contract with Locog and that it has been necessary to call upon the additional military personnel.
"In partnership with the military and Locog, we are working flat out around the clock to resolve the situation. We are determined that together we will deliver a successful and secure Games."
Mr Buckles has been asked to appear before the Home Affairs Select Committee next week.
Its chairman, Keith Vaz, said the G4S boss would have some searching questions to answer.
"The contract was signed two-and-a-half years ago and one would have expected them to put everything into it. We just don't know. We need to hear from them," he said.
"I think this is the right thing to do and this is a good basis upon which we can have a proper discussion when they come before us on Tuesday."
Patrick Mercer, a Conservative MP and former army officer, said the troops should get a bonus for their work, paid for by G4S.
"I think that would be a great gesture to the troops. And on top of that I think it might help G4S get out of a very difficult public relations trap," he said.
Former Labour security minister Lord West said the issue was not just about money.
He said: "It shows to me that G4S totally underestimated how difficult it would be to do the things they said they could do, and I think that should have been spotted a lot earlier."
Meanwhile, air security commander Air Vice-Marshal Stuart Atha said the RAF was ready to use "lethal force" if the Games were threatened.
He said a plane could be shot down as a last resort in a "worst-case scenario".
A series of airspace restrictions around London and south-east England came into force on Saturday morning and will last for a month.
Typhoon jets and Sea King helicopters are being deployed at RAF Northolt in north-west London.
The prohibited zone will be about 30 miles wide but does not affect commercial aircraft, which fly in established air traffic corridors.
It has emerged that 3,500 extra servicemen will be needed to provide security at the Games.
Culture secretary Jeremy Hunt said any serviceman who had been inconvenienced would have their costs repaid through refunds from the G4S contract.
G4S was contracted by the London 2012 Organising Committee to supply 10,400 staff out of the 23,700 security staff needed for the Games.
It said it had 4,000 people already working across 100 venues, with a further 9,000 people going through the final stages of training and accreditation.
Home Secretary Theresa May said it was discovered only on Wednesday, 16 days before the Games begin, that contractor G4S did not have enough trained security staff.
The 3,500 servicemen are in addition to 7,500 already agreed for venue security.
The head of London 2012, Lord Sebastian Coe, denied the Olympics was in "crisis".
"This is a seven-year project, every day is a challenge. Don't run away with the idea that this is a walk in the park. If it were a walk in the park everyone would be doing it," he said.
Shadow home secretary Yvette Cooper said the situation looked like "another Home Office shambles".