NEW YORK - Mayor Michael Bloomberg acknowledged Tuesday that the city pushed for a swift cleanup at the World Trade Center but said the fast pace was an effort to return remains to victims' families quickly.

Meanwhile, 36 more bone fragments were found Tuesday in subterranean cavities along the edge of the site as workers continued burrowing into areas that were apparently missed during the initial cleanup.

Port Authority police officers and workers at ground zero stand over a hole in the pavement on the West side of the site Monday, Oct. 23, 2006 in New York. [AP]

Bloomberg spoke a day after The Associated Press reported that some officials handling the cleanup in 2002 had recommended a more thorough search for remains but felt rebuffed by a city agency that just wanted to finish the job.

The agency in charge of the excavation, the Department of Design and Construction, was applauded for its efficiency in 2002 after it whisked away the 10-story pile of trade center rubble in less than a year.

"Were we under time pressure? Absolutely," Bloomberg said Tuesday. "I don't know any family member that didn't want to find out whatever they could about the loved one that they lost. And we did it as fast as we could, consistent with safety and completeness."

Some victims' relatives dismissed the mayor's explanation for the quick cleanup.

"It had very little to do with the families," said Monica Gabrielle, who has no identified remains of her husband, Richard. "This is another spin ¡ª it's a diversion away from the issue, which is that management failed, not the workers. And management needs to be held accountable."

Among the officials who said they raised objections during the nine-month recovery effort was Lt. John McArdle, ground zero commander for the New York Police Department.

"There came a point in time when they said, 'We gotta try to wrap this up,' and they tried to expedite it as much as possible, and they jumped the gun, and now you have all of these families hurt, and they're finding all these body parts," he said.

Several large bones were accidentally discovered last week after a utility crew opened up a non-working manhole. Since then, the city has been tearing up the pavement and examining other underground pockets in the same vicinity, which is a service road along the western edge of the 16-acre site.

In the past few days, more than 100 bones and fragments have been recovered. The medical examiner's office is working to match them to victims.

Thousands of pieces recovered during the main excavation still have not yielded matches, leaving more than 40 percent of the attack's 2,749 victims without any trace of remains.

The newly discovered bones are just the latest finding of overlooked remains. Hundreds of bone fragments have been found on the roof of a building just south of the trade center site, and officials are eyeing whether other buildings need to be combed again.