"My personal failings and imperfections have caused enormous pain to the people I love and I am truly sorry," said Fossella, a Republican, who lives in his Staten Island, N.Y., district with his wife and their three children.
Fossella is the only Republican member of Congress from New York City, and the paternity revelation could lead to the loss of a seat in Congress at a time when the House GOP faces the possibility of a second grim November of election setbacks.
House Minority Leader John Boehner said he expected Fossella to make decisions about his future in a matter of days, not months.
"I think Mr. Fossella is going to have some decisions to make over the weekend. And I would hope that, and frankly, expect that this is a decision between he, his family, and his constituents," Boehner said.
Fossella's private life came under scrutiny after he was arrested in the Virginia suburbs of Washington for allegedly driving drunk. Police said they stopped him after he drove through a red light.
When Fossella was pulled over, police said he told officers that he was going to see his daughter in the area. That prompted questions about who the daughter was.
"I have had a relationship with Laura Fay, with whom I have a 3-year-old daughter," Fossella said in his statement. It was Fay who got him out of jail after the arrest. She is a former Air Force lieutenant colonel and worked for a time as a liaison to Congress.
Police said Fossella's blood-alcohol level was twice the legal limit, and he could face a mandatory five days in jail if convicted. A court appearance on the drunken driving arrest that had been planned for next week was canceled, and he is now not expected back in court until June.
Fossella said he had no immediate plans to resign. The disclosures are a crushing blow to the career of a lawmaker once seen as a potential candidate for mayor of New York City. He faced a surprisingly tough re-election challenge in 2006, and Democrats have been hoping to unseat him this year.
"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. 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," he said.
There was little support from leaders of his party for him to remain.
A spokeswoman for the House GOP campaign committee said only that they expect the district to continue to elect conservative-minded lawmakers. A spokeswoman for the Democratic campaign committee declined to comment.
"He's politically dead. The only thing that hasn't happened is the autopsy report hasn't been written," said Doug Muzzio, a professor of politics at Baruch College in New York. "He can say he's going to stay all he wants, but come on ..."
Fossella, 43, was elected to Congress in 1997 in a special election to replace Rep. Susan Molinari, who resigned. His socially conservative positions squared nicely with his largely Catholic district. He serves as a member of the House Committee on Energy and Commerce.
Fossella's work in Congress shifted dramatically following the Sept. 11, 2001, terror attacks.
Hundreds of Staten Island residents died in the attacks, and Fossella became a prominent advocate for families of those killed.
As more recovery and rescue workers got sick after toiling at the ground zero site, Fossella pushed for Washington to pay for their health care an effort that has met with short-term success, but no long-term program.