"Bibi, you are talking about offenders?" the video asks. "And what about Arnaud Mimran?"
The video plays a recording of Mimran talking about his relationship with Netanyahu, saying "I know the Israeli prime minister personally. He was in my home."
The video then cuts to Netanyahu saying he received 100 million euro from Mimran for the 2009 elections.
Mimran was sentenced to eight years in prison in 2015.
Likud put out a video about Barak's connection to Epstein and the money he received from the Jewish American billionaire's foundation amounting to $2.3 million for research - which the video claims was never carried out.
"Barak has, until today, avoided revealing the research," the video proclaims.
On Monday, Barak attacked Netanyahu for a tweet he issued targeting Israeli journalist Guy Peleg for a quote he published from the ongoing investigation against the prime minister.
Netanyahu had attacked Peleg on Twitter for publicizing testimony about his use of sinus medicine on Channel 12, calling the quote "fake news."
Peleg responded in a tweet, saying "Mr. Netanyahu, let's tell the truth for once. You're the one who asked that this quote from Shefer's questioning be added in."
Barak used the opportunity to attack Netanyahu, tweeting: "The shame of the dweller of [the official residence of] Balfour has been revealed. Who would have believed that this is what the prime minister of Israel is dealing with?! As Netanyahu himself said about [former prime minister Ehud] Olmert: 'A prime minister who is buried up to his neck in probes cannot function ...' Sad."
The Twitter bickering is part of a burgeoning feud between Netanyahu and Barak. On Sunday, the two fought over Twitter, where Netanyahu posted an article about alleged pedophile and sex-trafficker Jeffrey Epstein, who was arrested on Saturday night in New York on sex trafficking charges. Netanyahu complained that the Israeli media was not criticizing Barak over his connections to Epstein.
Barak responded by turning the tables on Netanyahu.
“It pains me that people I know have gotten in trouble with the law,” Barak wrote on Twitter. “First came Netanyahu and now Epstein. I hope for both of them that the truth will come to light.”
Netanyahu began the social media battle on Sunday by calling Barak’s new Israel Democratic Party a joke, when speaking to supporters live on Facebook during a visit to a Jerusalem coffee shop.
Gil Hoffman and Yvette J. Deane contributed to this report.