The problems go well beyond last week’s news of a shortfall in the number of civilian guards for the Games that had been promised by a security contractor; the gap is now expected to be filled by Britain’s armed forces.

Newspaper accounts have told of recruits hired for essential security tasks at more than 100 sites — including the main Olympic stadium, which seats 80,000 — falling asleep during training sessions. Instructors for G4S, the private company that has a $440 million contract to provide 10,400 guards for the Games, have complained of facing rows of recruits who speak little or no English.

One tabloid published a photograph, which it said had been taken at a training session, that showed a young woman slumped at her desk, apparently sleeping, with a youth alongside her apparently listening to music through earphones.

The account, in The Daily Mail, told of recruits repeatedly failing to spot fake bombs and grenades during X-ray training, and clearing people through security during their training without spotting hidden weapons, in one case a 9-millimeter pistol stuffed into a “test spectator’s” sock. The paper quoted one whistle-blower, whom it described as having a military background, as saying that some of the people were poorly educated and unprepared: “Some of the people on that course you would not hire to empty a dustbin.”

Officials with knowledge of Olympic planning who asked not to be identified have said that some workers had been unemployed for months or years. Newspaper reports have also said that among those who have completed their training and been deployed to Olympic sites, dropout rates have been as high as 50 percent.

G4S, which has more than 650,000 employees in 125 countries, came forward on Saturday to offer an apology for not being able to provide enough security guards. The company’s chief executive, Nick Buckles, said in an interview with the BBC that it had realized only “eight or nine days ago” — more than six months after it signed a contract calling for it to provide 13,400 guards, with 3,000 as a back-up against dropouts — that it would not be able to meet its commitments.

“We deeply regret that,” he said.

Later, a company spokesman responded by e-mail to questions submitted by The New York Times that detailed the shortcomings alleged by whistle-blowers. The e-mail said the company was “working 24 hours a day to deliver on our London 2012 contract.” It said it did not tolerate people falling asleep or not paying attention during training.

It was more oblique on whether recruits failed to spot fake weapons during practice searches. “Some trainees have not worked as security officers before but by the time they have finished training they have been instructed in how to react when they spot items that are not allowed to be brought into venues.”

In the BBC interview, Mr. Buckles said he was “pretty sure” the guards already deployed could speak English well, “but I cannot say categorically as I sit here today.”

On Thursday, when the government acknowledged the extent of the bungling and announced that it would be adding 3,500 additional troops to the 13,500 troops already committed to security duties at the Games, it offered assurances that the security for the 17 days of competition would not be compromised.