Weiner told the New York Post he planned to "get back to work as best I can."
"I betrayed a lot of people and I know it," Weiner said. "I'm trying to get back to work now and try to make amends to my constituents and of course to my family of course."
Weiner was trying to put the scandal behind him despite ongoing calls for his resignation. At least nine Democratic leaders have joined an army of Republicans urging him to step down over the images he sent to various women via Twitter.
"Having the respect of your constituents is fundamental for a member of Congress," said Rep. Allyson Schwartz, D-Pa. The New York Times said Schwartz was overseeing the recruitment of Democratic candidates for the 2012 election cycle.
Weiner told the Post he had been completely forthcoming in his public statements about the scandal, but he declined to provide details on how it was affecting his marriage of less than a year to Huma Abedin, an aide to Secretary of State Hillary Clinton.
"Conversations between my wife and me are private, but you know, she's bearing up well and she's back at work and she's doing a great job," he said.
An NY1-Marist poll released Thursday indicated 56 percent of registered voters in Weiner's district think he should not resign, while 33 percent say he should and 12 percent had no opinion. If Weiner runs for re-election in 2012, 31 percent say they would definitely voted against him, while 30 percent said they would definitely vote for him and 38 percent said they were not sure.