Mahoney issued his statement hours after ABC News reported on its Web site that he had agreed to pay $121,000 in March to a former mistress and staff member after being threatened with a sexual harassment lawsuit. Mahoney said he would be vindicated.
House Speaker Nancy Pelosi also called for an investigation.
The network, citing unnamed current and former Mahoney staff members, said the congressman began his affair with Patricia Allen, 50, in 2006 while he was campaigning for Congress, promising to return morals to Washington.
On Tuesday, Mahoney read a statement with his wife, Terry at his side. He admitted he's caused "pain" in his marriage but denies paying hush money to a former aide to be quiet about an affair.
He says he takes "full responsibility" for his actions and the pain he caused his wife and daughter, but he did not directly admit having an affair.
Mahoney won the race after former Republican U.S. Rep. Mark Foley resigned when it was revealed he sent lurid Internet messages to male teenage pages who had worked on Capitol Hill. Foley was cleared of criminal wrongdoing by state and federal authorities.
Mahoney's bid to earn another term representing a district that has traditionally leaned slightly Republican was already considered one of the more competitive House races this fall.
Telephone messages left by The Associated Press for Mahoney and his congressional and campaign staff members were not returned Monday.
A Mahoney spokesperson told ABC that Allen resigned willingly and "has not received any special payment from campaign funds."
"While these allegations are based on hearsay, I believe that my constituents need a full accounting," Mahoney, who faces a Republican challenger in November's election, said in the release. "As such, I have requested the House Ethics Committee to review these allegations. I am confident that when the facts are presented that I will be vindicated."
Added Pelosi in her own statement: "These charges must be immediately and thoroughly investigated."
In addition to the cash payment, ABC News reported that Mahoney promised Allen a $50,000 a year job for two years at the agency that handles his campaign advertising.
That company, Nashville, Tenn.-based Fletcher Rowley Chao Riddle Inc., resigned from Mahoney's campaign later Monday.
"Tim Mahoney apparently included our company in a secret legal settlement without the knowledge of our firm. Our firm did not agree to any legal settlement," CEO Bill Fletcher said in a release. "If these allegations are true, Tim Mahoney's actions are unacceptable and not in line with FRCR's business ethics."
Mahoney is facing a stiff challenge in the November election. Former Army officer Tom Rooney, a lawyer whose family owns the Pittsburgh Steelers and a Palm Beach County dog track, is mounting a well-funded race aiming to win back the district for Republicans.
Rep. Rahm Emanuel of Illinois, chair of the House Democratic Caucus, heard rumors about an affair in early 2007 and confronted Mahoney, a spokeswoman said Monday.
"Upon hearing a rumor, Congressman Emanuel confronted Congressman Mahoney, told him he was in public life and had a responsibility to act accordingly and appropriately, and urged him to do so," the spokeswoman said. "They had no further conversations on this topic."
Friends of Allen's told ABC News that she wanted to end the affair, but Mahoney threatened to fire her is she did so.
"You work at my pleasure," Mahoney told Allen on a January 20, 2008 recorded telephone call, a portion of which was provided to ABC.
"If you do the job that I think you should do, you get to keep your job. Whenever I don't feel like you're doing your job, then you lose your job," Mahoney can be heard telling Allen.
"You're fired," he continued. "Do you hear me?"
Allen then asks why she is being fired, indicating there is another reason than her apparent inability to do her job.
"There is no why else," Mahoney responded.
"You're firing me for other reasons," Allen said on the call. "You don't, you're not man enough to say it. So why don't you say it."
Mahoney never admits to any affair in the portion of the tape obtained by ABC.
Allen did not return a telephone message from AP on Monday.
Allen's friends told the network that as part of the settlement, she was required to sign a letter of resignation indicating she left amicably.