Vito J. Fossella’s disclosure of a child born out of wedlock from an extramarital relationship left House Republican leaders uncertain what to say about his political future.

Fossella, R-N.Y., drew little support from Minority Leader John A. Boehner, R-Ohio. “I think Mr. Fossella is going to have some decisions to make over the weekend,’’ Boehner said Thursday. “This is a decision between him, his family and his constituents.’’

Fossella, a five-term lawmaker from Staten Island, was arrested for drunk driving in Alexandria, Va., May 1. In a statement Thursday, he acknowledged that he and a woman other than his wife have a 3-year-old daughter.

He hinted in the statement that he intends to serve out his term. “Over the coming weeks and months, I will continue to do my job and I will work hard to heal the deep wounds I have caused,’’ Fossella said.

The chairman of the House GOP’s campaign organization, Tom Cole of Oklahoma, said Republican leaders are giving Fossella time to deal with his family problems before broaching the topic of his political future.

But Cole said the party will be ready to defend Fossella’s seat if he resigns or decides not to seek re-election this fall.

“We’re not going to be caught flat-­footed,” Cole said. “We think we can win in a special election. If he were to choose to vacate, there would be adequate candidates on both sides.”

Whatever Fossella decides, it is now a safe bet that the 13th District seat will be hotly contested in November. Fossella was a Democratic target before his arrest, as a result of his relatively weak showing in 2006. He received less than 60 percent of the vote then against a severely underfunded Democratic opponent.

“This is a race that we’ve been targeting for a long time, and we believe that it’s a district that is certainly winnable,” said Carrie James, a spokeswoman for the Democratic Congressional Campaign Committee. “We’re ready for an election now, or we’ll be ready in November.”

Two Democrats are already seeking the nomination in the Sept. 9 primary. Stephen A. Harrison held Fossella to the lowest winning percentage of his House career in 2006, despite being outspent 10 to 1. Also running is New York City Council member Domenic M. Recchia Jr.

The names of several Republicans have been floated as possible replacement candidates should Fossella resign or retire, including Staten Island District Attorney Daniel M. Donovan Jr., state Sen. Andrew Lanza and New York City Council members James Oddo and Vincent Ignizio.

Fossella said in his statement that he and Laura Fay, a former Air Force officer, have a 3-year-old daughter. The congressman and his wife, Mary Pat, have three children of their own.

Fossella told police at the time of his arrest that he was on the way to visit his daughter. He is scheduled to appear in court May 12.

“My personal failings and imperfections have caused enormous pain to the people I love, and I am truly sorry,” Fossella said in his statement. “While I understand that there will be many questions, including those about my political future, making any political decisions right now are furthest from my mind.’’

First posted May 8, 2008 12:38 p.m.