City voters can expect no tax or fee increases through June 2007 if Mayor Bloomberg is re-elected, the mayor said yesterday during his first debate with the Democratic challenger, Fernando Ferrer.

Mr. Ferrer, trailing in recent public opinion polls by as much as 31 percentage points, attempted to take Mayor Bloomberg down a notch by attacking his ties to Republicans in Washington and his proclivity for forging “sweetheart deals” with developers.

The first matchup between Messrs. Bloomberg and Ferrer was heated at times, with Mr. Ferrer making an unusually concerted and aggressive effort to engage his opponent.

The candidates clashed on a number of issues – from taxes to affordable housing to education – but the fiercest battle of the debate yesterday morning erupted over guns.

In response to a question, Mr. Bloomberg acknowledged that shootings were up, even as other crimes had dropped significantly since he has been mayor. He then criticized the chairman of the Democratic National Committee, the former governor of Vermont, saying that Mr. Ferrer is “out campaigning with Howard Dean, who was eight times endorsed by the NRA.”

Mr. Ferrer shot back that Mr. Bloomberg supports President Bush and the Republican Party, which advocates for the right to bear arms. Mr. Bloomberg abruptly replied, “Not on this policy, I don’t.”

Mr. Ferrer implied that Mr. Bloomberg’s support for Republicans on some matters is the same as support on all matters: “You gave them money, Mike, and you can’t have it both ways, you can’t disclaim responsibility for the policies you politically and financially support.”

Mr. Bloomberg disagreed, calmly explaining to Mr. Ferrer: “I can’t have everybody in Washington vote for everything I like. I wish they would, but they don’t.”

Mr. Ferrer had the final punch of the “guns” round: “But you don’t have to support them, Mike, and you know what? You could do this city a big favor sometimes by putting your checkbook away.”

When asked whether he would undo any of Mr. Bloomberg’s initiatives if he were elected mayor, Mr. Ferrer said he would “halt” and “re-evaluate” the Atlantic Yards project, Forest City Ratner’s $3.5 billion proposal to erect more than a dozen offices, residential towers, a hotel, and a basketball arena in Brooklyn.

“I object to the lack of transparency, I object to the backroom deals, I object to the things we’re beginning to see emerge about a project that is becoming the twin brother of the West Side boondoggle,” he said, referring to the fight over the Jets Stadium on the far West Side of Manhattan.

Mr. Bloomberg snapped back that Mr. Ferrer’s stance countered that of an unsuccessful 2004 presidential candidate, the Reverend Al Sharpton.

“I couldn’t disagree more, and I think Al Sharpton, who supported my opponent, said it very well: This is about jobs for people in that community, this is about housing for people in that community, this is a project that has had enough scrutiny as anything,” Mr. Bloomberg said.

Throughout the debate, both candidates tried to portray themselves as tax cutters.

Mr. Ferrer said everyday New Yorkers want “a modicum” of tax relief so they can afford to live in New York.

“That’s why I’ll cut their taxes,” Mr. Ferrer said. “That’s why I’ll also provide 167,000 affordable homes and apartments. Those fees, those fines, those penalties do little to help middle-class and working-class people be able to live in their own neighborhoods, to be able to live decently in their own city – to be able to pass on dreams and hope and opportunity to their children, to their families.”

Mr. Bloomberg said that in his next term, New Yorkers can “expect to see a continued focus on doing more with less.”

“I would think for the next fiscal year, starting next July 1, if we focus on trying to do a little more with less, with the expansion of the economy, we will get through that year without any tax increases or fee increase,” Mr. Bloomberg said.

With Mr. Ferrer chuckling audibly in the background, Mr. Bloomberg said, “Freddy prefers $12 billion in extra spending and $6 million in tax increase already and he isn’t even elected.”

In almost every exchange, Mr. Ferrer played up his newly resurrected campaign theme of “Two New Yorks,” which he employed unsuccessfully in his 2001 mayoral bid.

Asked about whether he supported the financial incentive package that Goldman Sachs received when it agreed to move back to Lower Manhattan, Mr. Ferrer said: “There isn’t a better illustration of the two New Yorks than that deal.”

He continued, “In the Bronx, Xiomara Mejia lives in a hovel. If she’s late on her rent one month, she’s out on the street, but she’s been waiting two years for the city to force her landlord to make repairs. By contrast we can’t do enough to get Goldman Sachs from Midtown back to Lower Manhattan with a king’s ransom of $1.7 billion in tax abatement.”

Mr. Bloomberg said the city gave Goldman Sachs the minimum amount needed to make sure the bank did not move to New Jersey.

“If there’s any administration that’s not been willing to give tax breaks willy-nilly to companies it’s our administration we’ve given virtually none,” Mr. Bloomberg said. “This is the one case where I really thought they could have moved and it might have been in their economic interest to move, and we want to keep those jobs here.”

When it came to education, Mr. Ferrer repeatedly suggested that the mayor cares about test scores to the detriment of learning. He also suggested that the mayor’s focus on elementary school students has contributed to the city’s high-school drop-out woes. “Look, I’m not running to be the mayor of the fourth grade,” Mr. Ferrer said. “I’m running to be the mayor of all the grades.”

Mr. Bloomberg said the four year graduation rate in the Bronx had increased to 52% from 40% during his administration. “In the city as a whole after decades of doing nothing, it’s gone from 50% to 54%,” the mayor said.

All in all, experts said Mr. Ferrer’s performance, while topping expectations, wasn’t powerful enough to change voters’ minds.

“Debates move numbers in significant ways when a candidate makes mistakes or has an over-the-top success,” a professor of public affairs at Baruch College, David Birdsell, said.

Mr. Birdsell said Mr. Ferrer was unable to “rattle” the mayor.

“I think Michael Bloomberg did what he had to do to make sure there was no commanding story line coming out of the debates,” he said. “He maintained his equanimity throughout the debate.”

At this point, he said, with a week to go and a gap as large as it is, a come-from-behind victory by Mr. Ferrer “would be truly unprecedented.”

Mr. Ferrer faced off against the Conservative Party’s candidate in the mayoral race, Thomas Ognibene, earlier this month in the first Campaign Finance Board-sponsored debate. The mayor skipped that debate, waiting to take on his Democratic rival until only days remained before New Yorkers head to the polls on November 8.

Mr. Ognibene was not included in yesterday’s debate. He told The New York Sun that he ran errands yesterday morning rather than watching the exchange between his political rivals.

The next debate will be Tuesday at 7 p.m. on WNBC, channel 4.