The move, just a fortnight before the Games, is potentially a major embarrassment for organisers Locog.
The overall 23,700-strong security force for the Games will include a mix of military and private security guards and at least 3000 unpaid London 2012 volunteers who will be used at the beginning of the security process.
A G4S spokeswoman said: "This has been an unprecedented and very complex security recruitment, training and deployment exercise which has been carried out to a tight timescale.
"We have encountered some issues in relation to workforce supply and scheduling over the last couple of weeks, but are resolving these every day and remain committed to providing a security workforce for the start of the London 2012 Games."
The spokeswoman continued: "Our planning with Locog and other security agencies allows for a variety of contingencies which have been reviewed in the build-up to the Games.
"We accept that the Government has decided to overlay additional resources. We remain committed to keep London 2012 safe and secure."
Home Secretary Theresa 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 Games, she told MPs.
Some 13,500 troops are already involved in a wide variety of Olympics-related roles across the UK, including 7500 for venue security.
The latest move will boost the number of servicemen and women involved in venue security to 11,000 and the overall number of troops involved in the Olympics to some 17,000, it is understood. As well as providing venue security, military personnel will also be involved in specialist support roles including air security, search teams, communications and logistics, among others.
Shadow Olympics minister Dame Tessa Jowell said yesterday: "With two weeks to go to the start of the Games, it is imperative that action is taken to ensure that the full and necessary quota of security personnel are in place so that the Games will be safe and secure.
"But this is clearly a serious problem, and we have to understand how this problem arose.
"We need to know why the problem has emerged so late in the day and precisely what has been agreed to."
She added: "We also must know whether this affects Army commitments elsewhere, which units are providing people and what terms and conditions are given for those who will likely lose periods of leave."
A London 2012 spokesman said: "Security for the Games is big and complex but we have the best brains in the security business working on this – the Home Office, Metropolitan Police, Ministry of Defence and the world's largest private security business.
"Delivering a safe and secure Games is everyone's number one priority. We do not anticipate an increase in the overall venue security numbers."