The 1 minute video was posted on his campaign's website Tuesday evening. Speaking directly into the camera, the former congressman addresses politicians and newspaper editors who have said he should quit.
He says they don't know New York or him.
"Quit isn't the way we roll in New York City. We fight through tough things. We are a tough city," Weiner said in the video.
Last week, Weiner acknowledged exchanging sexually explicit messages online after similar behavior spurred his resignation from Congress in 2011. He says in the video that when "embarrassing" things in a person's private life become public, the person should talk about it.
A new poll released Monday found Weiner's support fell from 26 percent last week to 16 percent.
(The Associated Press contributed to this report).