NEW YORK (AP) _ Mayoral candidate Rudolph Giuliani has ignited the flashpowder of city politics, flaring racial and religious tension as he struggles to wrest Jewish voters from his black Democratic opponent.

While Giuliani's first-time candidacy has been dogged by missteps, the latest controversy is heightened by his unabashed intent to win Jewish votes by linking his opponent, David Dinkins, with Jesse Jackson.

''It is a naked effort to play on Jewish fears,'' Rabbi Balfour Brickner, a liberal Jewish leader, said Friday. ''The net effect of what he's doing is to increase racial polarization. It's a contemptible low blow.''

At issue is an advertisement placed by Giuliani in this week's edition of the city's largest-circulation Yiddish newspaper, The Algemeiner Journal. It shows two photos: in one, Giuliani, a Republican, with President Bush; in the other, Dinkins, the Manhattan borough president, with Jackson.

The text says: ''Let the people of New York choose their own destiny.''

The ad intensified a rift in the city's Jewish community, which made up the largest proportion of white voters for Dinkins in the Sept. 12 primary, when he unseated three-term incumbent Mayor Edward I. Koch.

On one side are critics such as Brickner, who said the ad plays unfairly on Jewish suspicions of Jackson, who supports Palestinian self-determination and once called New York ''Hymietown,'' for which he later apologized.

Giuliani ''suspects that Jews hate Jesse Jackson and he's playing on that hatred and that fear,'' said Brickner. Dinkins, he noted, has a history of supporting Israel, Soviet Jewry and other Jewish causes.

Yet others, such as Eli Blachman, associate editor of The Algemeiner Journal, called the ad fair play. ''It shows who Giuliani's surrounded with and who Dinkins is surrounded with,'' he said. ''There's no words of racism. It just says the people have to decide.''

Jackson, in Puerto Rico surveying damage from Hurricane Hugo, said he didn't want to comment on the ad placed by Giuliani, but he praised Dinkins' mayoral campaign.

''I don't want to violate the integrity of this mission (to the Caribbean) discussing New York politics,'' Jackson said. ''But Dinkins is doing a very effective campaign, appealing to the hopes and not the fears of the people.''

According to polls, 22 percent of New York City's 3 million registered voters are black and 18 percent are Jewish. Of the total, about 2 million are Democrats.

The message came at a moment of heightened sensitivity. Racial tensions arose here in August after a white gang killed a black youth in Bensonhurst, Brooklyn - a killing reminiscent of a 1986 racial attack in Howard Beach, Queens.

Then Jewish comedian Jackie Mason, a Giuliani supporter, suggested in an interview published this week that Jews were supporting Dinkins as a result of Jewish ''complexes,'' and said blacks had rarely backed Jewish causes.

The Jewish Community Relations Council demanded repudiation of those remarks, saying the election ''should not be dragged into the gutter,'' and the Giuliani campaign dropped Mason. The comedian apologized on Thursday.

The council, an umbrella group of Jewish organizations, did not directly criticize the Giuliani advertisement. Among Jews, ''Some consider it to be legitimate and some consider it to be illegitimate,'' said Michael Miller, the council's director. ''It raises a lot of emotions.''

Properly or not, Miller said, Giuliani has raised a double-edged sword, risking alienating some Jews while he attracts those who fear Jackson's role in a Dinkins mayoralty. ''The Jewish community is not a monolith,'' he said.

Some analysts said the ad marked a necessary, if risky, step for Giuliani, who trails Dinkins by more than 20 percentage points in the polls and must overcome a 5-1 Democratic edge in voter enrollment to win on Nov. 7.

''Giuliani doesn't have the Jewish vote and he wants it,'' said Brickner. ''He thinks he needs it to win, and he's right. He's reaching out to the Jewish vote, grasping at it with every gimmick and tool he can use.''

Giuliani's strategists defended the approach.

''This ad has absolutely nothing to do with race. It has to do with who are the political supporters of the candidates,'' said Ken Caruso, Giuliani's deputy campaign manager.

''It's a very fair question to ask what Jesse Jackson's role will be in a David Dinkins administration,'' Caruso said. ''It's the Dinkins campaign that brought Jesse Jackson here.''

Dinkins was state co-chairman of Jackson's 1988 presidential campaign. Jackson campaigned in black neighborhoods for Dinkins, albeit sparingly, late in the primary race, and he spoke at Dinkins' primary-night celebration.

Friday, Dinkins called Jackson ''my friend,'' reiterated his support for Israel and said of Giuliani's ad: ''I know what he's trying to do. I'd prefer that people would say and do things designed to bring people together, rather than divide them.''

Yet Blachman, the newspaper editor, said divisions already exist.

''Out the street I hear constantly that people are worried about the Jesse Jackson business,'' he said. ''They think Dinkins is a very nice fellow. If Jesse Jackson wasn't around him, he wouldn't have a problem with the Jewish people.''