Chief executive Nick Buckles told MPs the company would not bid for the contract for the next football World Cup or Olympics, both due to be held in Brazil.
However, last night G4S would not rule out the possibility of a bid for the Glasgow Games, which are due to be staged in two years' time.
The organisers, Glasgow 2014, said that all companies would have their bids "considered on their merits".
G4S is one of the largest security firms in the world, employing around 650,000 staff.
But yesterday the controversy over its failure to deliver on its £250 million Olympics contract continued to grow.
With less than a fortnight to go before the Games open, the site of one of the first big events, Box Hill in Surrey, was hit by a shortfall in G4S staff.
MPs were told that the company expected to provide less than half the staff needed on the route of the men's road cycling race, due to take place on July 28.
On another dramatic day of developments, Mr Buckles told members of the Commons Home Affairs Committee that once the Games were up and running police could be given as little as three days' notice that they would be needed to protect events.
But he insisted that his company would still collect its £57 million management fee.
Mr Buckles, who once famously declared his motto was "no excuses", said he had only been made aware of the problems two weeks ago, while on holiday in America, which committee chairman Keith Vaz described as "astonishing".
He also admitted that he did not inform the Home Secretary until a week later and the Stock Exchange until two days after that.
Mr Buckles added that G4S was hoping to provide 7000 staff for the Games, but admitted that only half have already been trained.
But despite the catalogue of problems, G4S last night refused to rule out bidding for the contract for the Glasgow Games.
A spokesman for the company said: "At the moment we are committed to, and focusing our attention on, delivering a safe and secure (Olympic) Games."
A spokesman for Glasgow 2014 said that with two years to go, the organisers were in the "early stages" of procuring the security provision.
He said: "Companies bidding for contracts will be considered on their merits and assessed in line with detailed tendering requirements and procedures.
"Identifying lessons from the London 2012 Olympics will play a role in helping the Glasgow 2014 Organising Committee to deliver an outstanding athlete-centred, sport-focused Games."
Earlier, under pressure from MPs, Mr Buckles also pledged to cover all the costs of the troops and police officers who have had to be called up to protect the Games.
He said he was prepared to consider paying an "Olympics bonus" to those who have been called up.
In an extraordinary appearance, he said that he was "deeply sorry" for the problems, which he went on to admit were a "humiliating shambles".
The chief executive, who earns more than £800,000 a year, also said he regretted signing the contract to provide more than 10,000 security staff.