Weiner said he plans to get back to work on behalf of his New York district.
The seven-term lawmaker has come under pressure from several Democratic colleagues to resign after he admitted to sexually explicit online relationships with women.
"As a woman, as a member of Congress, as his colleague, I think the right thing to do for Congress, for his constituents and for the American people, is to resign his position," said Rep. Allyson Schwartz of Pennsylvania.
House Minority Leader Nancy Pelosi called for an ethics committee investigation to determine whether Weiner's actions violated any House rules.
One person who seems to be sticking by Weiner is his wife 35-year-old Huma Abedin, who is thousands of miles away from the tawdry controversy. She is traveling in the Middle East with her boss and close friend - Secretary of State Hillary Clinton.
Abedin has a reputation for being unflappable, loyal and utterly discreet. But now she has been thrust into the spotlight by her husband's behavior.
"Huma is one of the world's most intriguing, interesting, high-profile women who we really don't know," said Lois Romano from Newsweek.
Abedin is three months pregnant, sources told ABC News, and she is leaning on close friends during this difficult time - especially Clinton, who has noted the painful déjà vu for both of them.
Abedin initially believed Weiner's story that someone had hacked into his /*Twitter*/ account. She is reportedly devastated by her husband's admission to sending lewd photos of himself to several women and engaging in risqué online chats.
After vehemently defending himself last week, Weiner is laying low, working on an apology tour behind the scenes to try and save his job.