The existing law limits city officeholders to two consecutive four-year terms. Voters set the limit in a 1993 referendum and reaffirmed it three years later.
Both sides traded accusations that City Hall was stacked with paid supporters and not people who attended for their own reasons.
A spokesman for the mayor said all supporters who were urged to attend on the mayor's behalf were recruited as volunteers.
Among those who spoke in favor of Bloomberg's plan were former Gov. Mario Cuomo, who has long opposed term limits, and former Mayor Ed Koch, who served three terms before the current limits were set.
Cuomo said term limits are "a desperate attempt to improve governance," arguing that voters can get rid of elected officials simply by voting them out of office.
He had a testy exchange with City Councilman Charles Barron, who does not support Bloomberg's bid to change the law. The councilman said term limits are often necessary to neutralize the incumbent advantage.
Other council members who oppose Bloomberg's effort said repeatedly that they do not disagree with the idea of changing the term-limit law but do not believe it should be done without voter input.
"Whether or not you are for or against term limits is not the issue," said Councilman David Weprin. "The issue is not term limits, but rather the process. The people have spoken, and it should remain in the hands of the people."
Bloomberg did not attend the hearing. At a separate news conference Thursday, he dismissed the opposition as a "handful of people" who manage to seem like a bigger group because of their determination and organization.
Along with Bloomberg's proposal, a City Council committee was also considering two bills intended to thwart the mayor's effort.
One would require voter approval for any change to the term-limits law. The other would establish a commission to evaluate the issue and perhaps put it on the ballot.
The spirited hearing Thursday was the first of two public meetings on the issue, and another was set for Friday. The full council is not expected to vote until next Thursday, at the earliest.
