The extra troops are in addition to the 13,500 who are already being brought in for the games and news of the reinforcements comes amid fears private contractor G4S will not be able to provide enough trained staff in time.
G4S said it had "encountered some delays" in processing applicants through the final stages of training.
Keith Vaz, the Labour chairman of the Home Affairs Select Committee, tabled an urgent question to the government on Olympics security after earlier saying he would write to the home secretary for an explanation. He said he was "deeply concerned" that G4S were unable to deliver their contract and that "the Home Office have left contingency plans to the last moment". Mr Vaz said he had also asked G4S's chief executive and chairman to appear before the committee next week.
Soldiers serving with the British Army in Germany have had their notice to move shortened and could be transferred to the capital in days. Former soldier and Conservative MP Patrick Mercer, whose report on Olympic security is published today, described the announcement as ‘extraordinary’.
"In one breath the government can cut the army and in the next it orders 3,500 troops to be magicked out of nowhere," he said.
G4S is being paid £300million but has not been able to guarantee it can supply the 10,000 civilian guards it is contracted to deliver, reports say. A spokeswoman blamed issues with ‘workforce supply and scheduling’ and accepted the addition of extra troops.
Mrs May was forced to defend G4S in the Commons on Monday, saying she was ‘confident our partners will deliver a safe and secure Games’. More than 100 different venues need to be protected during the Olympics, she told MPs.
According to the company,"We have encountered some delays in progressing applicants through the final stages but we are working extremely hard to process these as swiftly as possible."Â We understand the government's decision to bring in additional resources and will work with Locog, the military and other agencies to deliver a safe and secure Games.