Mayor Bloomberg’s approval rating has risen in the past three months, but he still trails one mayoral contender, Fernando Ferrer, a poll released yesterday indicates.

The proportion of respondents who said they approved of Mr. Bloomberg’s performance in office jumped to 49%, up five percentage points since the last poll 11 weeks ago and 18 points since his all-time low in July 2003. The poll, which was conducted by Quinnipiac University, found that 39% disapproved of the freshman Republican’s job performance.

Mr. Ferrer, the former Bronx borough president who finished first in the 2001 Democratic mayoral primary but lost to Mark Green in the runoff election, has consistently polled better than the mayor. In the Quinnipiac poll conducted November 5-8, he had 45% to Mr. Bloomberg’s 40% in a head-to-head matchup. But the spread between them has narrowed by two percentage points since the poll taken before the Republican National Convention.

The new poll found that 64% of African-Americans and 59% of Hispanics favored Mr. Ferrer, who is Puerto Rican, over Mr. Bloomberg, who is white and Jewish.

Both men responded with caution yesterday, saying the only results that matter are the Election Day returns.

“I take all these polls with a grain of salt,” Mr. Ferrer said during a phone interview. “They are what they are given that we’re a year away.

“But,” he continued, “it’s very nice to get the kind of support I am apparently getting across the neighborhoods and boroughs of this city and across diverse groups of this city.”

Mr. Bloomberg predicted that he would be back for a second term if the city continues to be on an upswing. A combined 58% of the 1,221 people surveyed reported being either “very satisfied” or “somewhat satisfied” with things in New York.

“The only poll that matters, keep in mind incidentally, is the one that’s going to be taking place on November 8, 2005, and that’s the poll that I hope comes out well so that I can have an opportunity to continue to make the changes that I think most people in this city want to see made,” Mr. Bloomberg told reporters on the Lower East Side, where he was making an announcement about new playgrounds the city is creating.

After the mayor first took office, his approval rating hovered between 57% and 65%. It dropped sharply during the city’s budget crisis, which led to the closing of firehouses and the slashing of services, and when the city increased property taxes.

“The beginning was a honeymoon for him,” the director of Quinnipiac’s Polling Institute, Maurice Carroll, said. “That lasted until the property tax and the budget. But now he’s almost 50% again, the magic number.”

Though the mayor still has lower approval ratings among members of minority groups, he seems to be chipping away at the image that he cannot relate to the average New Yorker. In the latest poll, 45% said the billionaire mayor, whose net worth is said to be $5 billion, cared about their problems and needs – up three points from the last snapshot and his highest score on that question since October 2003. A strong majority of participants, 65%, said he had strong leadership skills.

Besides Mr. Ferrer, Mr. Bloomberg outpolled all of the other Democratic contenders in head-to-head match-ups – though by modest margins. The Manhattan borough president, C. Virginia Fields, won 38% support compared to Mr. Bloomberg’s 42%.

The speaker of the City Council, Gifford Miller, the city comptroller, William Thompson Jr., Council Member Charles Barron, and Rep. Anthony Weiner fared less well, but with the primary still 10 months away, they cannot be counted out.

When the 754 Democratic respondents were asked to pick a candidate for mayor, Mr. Ferrer was the choice of 28%, which was only one percentage point higher than “Undecided” but twice the percentage who named Ms. Fields and about three times the percentage who preferred Messrs. Thompson, Miller, and Weiner. Mr. Barron was the choice of 3% of the Democrats in the poll by the Connecticut university. None of the top Democratic contenders has officially declared candidacy.

Mr. Carroll called Mr. Ferrer “the one to beat,” noting that he has the most name recognition because he’s already run in a citywide election.

The poll’s margin of error is plus or minus 2.8 percentage points. The margin of error on questions posed to the Democratic respondents is 3.6%.

The poll found that 68% of participants disapproved of President Bush, whom the mayor has tried to distance himself from, and that 62% thought Police Commissioner Raymond Kelly was doing a good job.