(CNN) - A week after claiming a hacker had posted a lewd photo to his Twitter account, U.S. Rep. Anthony Weiner on Monday apologized for lying about the incident and admitted carrying on inappropriate relationships with several women he'd met online.

Weiner, a New York Democrat, said he is not resigning his seat, nor is he planning on separating from his wife. But he said he took "full responsibility" for his actions - both the relationships and for lying about sending the photo last month of his bulging underwear on his Twitter account.

"To be clear, the picture was of me, and I sent it. I'm deeply sorry for the pain this has caused my wife, and our family, my constituents, my friends, my supporters and my staff," he said, claiming he'd posted the Twitter photo accidentally as a "joke" and then "panicked." "I lied because I was ashamed at what I had done, and I didn't want to get caught."

An emotional Weiner described his actions as "dumb," "destructive" and "deeply, deeply hurtful" - both for his admitted coverup and for repeatedly engaging in "inappropriate conversations conducted over Twitter, Facebook, e-mail and occasionally on the phone" with women he'd met online, mostly via Facebook.

The congressman claimed that he never met any of these women in person, and that his wife Huma only learned he'd been lying about the Twitter picture on Monday morning.

"I have made terrible mistakes," Weiner told reporters. "I have not been honest with myself or my family. ... I should not have done this, and I should not have done this particularly when I was married."

Weiner claimed he does not believe he used any government resources, while he "exchanged messages and photos of an explicit nature with about six women over the last three years." Some of those relationships began before his 2010 marriage and some happened, and continued, afterward.

Still, House minority leader Nancy Pelosi announced that she would call "for an Ethics Committee investigation to determine whether any official resources were used or any other violation of House rules occurred."

Weiner issued a statement saying he would "welcome and fully cooperate" with the probe, which other Democratic leaders also rallied behind. But one Republican source called the move "hollow," saying Pelosi should have insisted that Weiner resign - as former Rep. Chris Lee, a New York Republican, did in February amid reports that the married man had tried to solicit women via Craigslist.