In an ominous sign for Rep. Vito Fossella, the campaign arm of the national Republican Party is refusing to support him publicly.

When asked to comment on the race in New York’s 13th District, which includes Staten Island and parts of Brooklyn, a spokeswoman for the National Republican Congressional Committee, Julie Shutley, said only that voters in the district “believe in national security and lower taxes” and will reject Democratic policies.

She would not say whether the committee had endorsed the candidacy of Mr. Fossella, the Republican incumbent who was arrested last week on drunken driving charges.

The statement marks a significant departure for the party, which generally supports its incumbent lawmakers. Just last month, Vice President Cheney headlined a fund-raiser in New York for Mr. Fossella, who is facing a challenge by two Democrats, Stephen Harrison and a City Council member, Domenic Recchia.

The Washington Post reported yesterday afternoon that Republican insiders say there is little chance Mr. Fossella, who has spent more than a decade in Congress, will seek re-election.

Last week, Mr. Fossella was arrested for drunken driving in Alexandria, Va., with a blood alcohol content level of 0.17%, more than twice the legal limit. If convicted, he faces a mandatory five-day jail term.

Compounding his troubles is a growing focus on Mr. Fossella’s relationship with a woman who reportedly picked him up from the police station after his arrest, Laura Fay, and his relationship with her young daughter.

When Mr. Fossella was pulled over, he told police that he was driving to see his sick daughter on nearby Grimm Street — where Ms. Fay lives with her daughter, the Daily News reported. The congressman’s wife and three children live on Staten Island.

Two Republicans, Council Member James Oddo and the district attorney of Richmond County, Daniel Donovan, have been mentioned as possible candidates for the 13th District seat, should Mr. Fossella step down or decline to run again.

A spokesman for Mr. Donovan said it is too early to make any projections about the district attorney’s political future or the congressman’s.

When Mayor Bloomberg was asked yesterday whether Mr. Fossella should run for re-election, given reports in the press, he said he had “no idea.”

“You see stuff in the paper, I don’t know whether it’s true or not. I’ve not talked to Congressman Fossella in a few weeks and certainly not talked to him about this,” Mr. Bloomberg said. “Congressman Fossella has worked hard for this city. He obviously did something that I think is wrong, and I think he said that he shouldn’t have done it and he thought it was wrong in retrospect.”

A spokeswoman for Mr. Fossella did not return calls for comment.