Firefighters said city officials want to save money
Firefighters broke through police lines at Ground Zero, the spot marking the remains of the World Trade Center, before holding a moment's silence in the wreckage.
Five policemen were injured.
Early on Saturday, the Manhattan District Attorney charged 10 of the firefighters with obstruction of governmental administration, disorderly conduct and trespassing - all misdemeanours.
Two other men arrested were not charged.
There was reported to be applause in court for the firefighters after their appearance.
They are to appear for another hearing on 18 December. At a press conference later in the day, Captain Peter Gorman, president of the Uniformed Fire Officers Association, said that relatives and co-workers of the 265 firefighters and rescue workers that died do not want their bodies destroyed by the recovery process.
"You wouldn't excavate a cemetery or sacred burial ground like that. Why would you do that with 5,000 citizens of this country buried down there?" he said.
'Unacceptable' behaviour
"The kind of conduct displayed today is unacceptable," said Mr Giuliani.
"You can't hit police officers, you can't disobey the law and you have to have enough professionalism and dignity about yourself to not conduct yourself in that way."
Firefighters say unless they continue with the search for bodies, many human remains will end up discarded along with tons of rubble being removed by construction workers.
Mr Giuliani said he wanted to reduce the recovery team from about 100 to 25 because the site was becoming increasingly dangerous.
"Here's what we have to make sure doesn't happen - that we don't have any more fatalities there, that we don't lose any more lives there," he said on Friday.
Firefighters say the mayor's decision has more to do with money, with millions of dollars being paid in overtime to their men who have been working round-the-clock since the twin towers were destroyed on 11 September.
Many protesters held placards and chanted: "Do the right thing", as union leaders using loud hailers criticised New York City officials.
A senior police officer appealed for the firefighters to calm down, telling them: "This is not a confrontation."
Later Fire Commissioner Thomas Von Essen apologised to the injured officers on behalf of the fire department.
But some firefighters have called for his resignation, accusing him of a dictatorial style that has alienated many rescue workers.