Mayor Michael Bloomberg acknowledged Tuesday that those who handled the World Trade Center cleanup years ago worked "as fast as we could" but said that was because the city was urgently trying to get remains back to the families after the Sept. 11, 2001 terror attacks.

Meanwhile, more bones 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.

Bloomberg spoke a day after The Associated Press reported that some officials handling that project in 2002 had urged for more remains searching but felt rebuffed by a city agency that just wanted to finish the job. The emotions and disagreements from years ago have new significance now that remains are turning up at the site, as well as atop a nearby skyscraper.

The agency in charge of the excavation, the Department of Design and Construction, was applauded in 2002 for the efficient way it pared down and whisked away the ten-story pile of trade center rubble in under 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 in 2002.

"It had very little to do with the families," said Monica Gabrielle, whose husband Richard was killed and has no identified remains. "This is another spin — 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 told the AP about the objections they raised 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, from nearly every part of the body. The medical examiner's office is working to match them to victims. The remains for more than 40 percent of the 2,749 victims still have not been identified.

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 sitting just south of the trade center site, and officials are eyeing whether other buildings need to be combed again.