The 1,200 military personnel come on top of 3,500 already called up specially this month after security contractor G4S said it would not be able to supply the number of guards it promised. The Games begin Friday.
Hunt said last Thursday that there was no need to deploy extra troops but that putting 1,200 on standby means they can be moved within 48 hours rather than seven days if required.
He said then that G4S was showing progress in recruiting and accrediting staff.
The chief executive of G4S, Nick Buckles, faced a grilling last week by lawmakers furious about the security situation.
British lawmakers forced Buckles on July 17 to agree that the fiasco is "a humiliating shambles."
Buckles said the company should not have agreed to provide 10,400 guards for the Olympics, six days after the security giant admitted it could not do so.
"We regret signing the contract," Buckles said under pressure from lawmakers.
The company's failure forced the government to call in 3,500 extra military personnel to help.
"We are constantly reviewing the extent of the G4S shortfall and the military contingency force," the Home Office said before the extra 1,200 were deployed Tuesday. The total UK military deployment at the London 2012 Olympics is 18,200, according the government's Olympics communications office.
G4S has a £284 million ($444 million) government contract to provide security staff for the Olympic Games.
As of his questioning by lawmakers a week ago, only 4,000 guards were trained and ready, he said.
Buckles said there was a company "expectation" that 7,000 will be ready by the time the Games begin, although he called the exact number "a moving target."
Labour lawmaker David Winnick laid into Buckles, insisting several times that the snafu was "a humiliating shambles."
Buckles finally said he could not disagree.
The company will reimburse police forces that have to provide officers to cover for G4S shortfalls, and will "consider" paying bonuses to military and police who are called in to help, he said.
The company accepts "100% responsibility" for its failure, and is "extremely grateful to the military and police for helping us out," Buckles said.
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The G4S recruits are supposed to perform tasks including venue perimeter security, such as manning X-ray machines, searching people, searching vehicles and operating closed-circuit television systems, G4S said Sunday.
G4S has said that it stands to lose up to $77 million after failing to recruit enough staff.