US authorities had been investigating reports he sent explicit messages previous year to a teenage girl in North Carolina.
Weiner was released on bail and will be sentenced on September 8.
The investigation led FBI agents to seize Weiner's laptop computer, which led to the discovery of a new cache of emails that then Democratic presidential candidate Clinton sent to Abedin.
Intending to send a private message to a young woman, Weiner accidentally sent out an explicit picture of himself on his public Twitter feed.
While running for New York City mayor in 2013, more messages surfaced, burying his attempt to resurrect his political career.
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Last year, when Weiner got caught sending yet another underwear selfie, with their then-three-year-old Jordan asleep at his hip, Abedin had still refrained from divorce.
The judge also told Weiner he would have to register as a sex offender.
The Democratic former congressman apologized to the 15-year-old, saying, "I have a sickness, but I do not have an excuse".
Former congressman Anthony Weiner admitted in court Friday to sending sexually explicit messages and photos to a 15-year-old girl, PEOPLE confirms.
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Weiner was already in federal custody ahead of the hearing.
During that federal investigation, at least one device used by Weiner and Abedin was discovered.
In 2011, while serving in Congress, he accidentally tweeted to the world a photo of his boxer-clad erection. The Comey letters and late-in-the-election investigation have been blamed for Clinton's loss to President Donald Trump, The Los Angeles Times reported.
Crain's New York Business contributed to this article.
He went on: "This fall, I came to grips for the first time with the depths of my sickness".
He also apologized to his victim, "whom I mistreated so badly".
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