"I don't know what I was thinking," Weiner, 46, said during a news conference in New York on sending photos over social media and engaging in six inappropriate online relationships in the past three years.
He said his wife of less than a year, Huma Abedi, knew of some of the online relationships but told her only Monday morning about tweeting the raunchy photo.
"I love my wife very much," he said, "and we have no intention of splitting."
"I take full responsibility for my actions," Weiner said. "I made terrible mistakes … and am deeply sorry."
The seven-term congressman said he would "try to handle this," and didn't rule out seeking professional help.
He said he meant to send the photo "as part of a joke" in a direct message to a woman in Seattle, but accidentally posted it publicly on Twitter. He said he took it down, said his account was hacked, and then "I stuck with the story."
"To be clear, the picture was of me and I sent it," he said. "This woman was unwittingly dragged into this and bears no responsibility."
"I haven't told the truth; I have done things I deeply regret," Weiner said, sometimes choking with emotions. "I brought pain to people I cared about the most and people who believe in me."
"I deeply regret what I have done," the representative said. "But) I am not resigning."
He said he spoke Monday with House Democratic Leader Nancy Pelosi, who told him to come clean.
"I don't know what I was thinking," he said of his online actions. "This was a destructive thing to do."
He said he was unaware of using any government-issued equipment to conduct his questionable online activities.
"I regret not being honest about this. I was embarrassed, humiliated. I really regret it," Weiner said about lying about his inappropriate online relationships and sending the blue photo. "This was a mistake. I'm very sorry for it."
He repeatedly apologized to his wife, family, staff, constituents and media for lying about the tweet.
"Anyone who was misled, people whom I lied to, I have an apology for all of them," he said. "I treated it as a frivolous thing, not acknowledging it as causing harm to so many people."
He said he doesn't believe his actions violated any laws or oath to his constituents, but "represent a deep personal failing."
Whether he returns to Congress depends on his constituents.
"It's up to my constituents," Weiner said. "I will work hard to win back their trust and confidence."
But, he said, "The last thing I'm thinking about … is an election next year."