Anthony Weiner -- Some Sexting Happened AFTER My Resignation

NYC mayoral candidate and self-admitted Internet perv Anthony Weiner says he continued to engage in SEXTING other dirty sex stuff AFTER he resigned from office.

Weiner said the most recent sexting incident took place last summer.

Weiner says the sexting "is entirely behind me now" ... and he will not drop out of the race for NYC mayor.

Weiner's wife Huma Abedin -- who looked SUPER UNCOMFORTABLE during the event -- also addressed the media ... and said she decided to stay married to Weiner because she felt it was the best decision for the family.

"I have forgiven him, I believe in him and as I have said from the beginning we are moving forward," Huma said.

During the media conference, a creepy guy behind a cubicle kept popping up behind Weiner like a whac-a-mole. At one point, the guy waved ... it was pretty hilarious.

Weiner initially called for the news conference to address the latest allegations -- first reported by TheDirty.com-- involving lewd photos and chat messages he sent to a 22-year-old girl on the Internet in 2012.

Weiner resigned from Congress in 2011.

Weiner has already released a statement admitting the chats were real ... but didn't say whether the Internet affair actually occurred in the wake of his infamous 2011 sexting scandal, as the 22-year-old woman is claiming.

Weiner said, “I said that other texts and photos were likely to come out, and today they have."