Labor MPs who left the party should "resign and stand for election," said Jeremy Corbyn.
In a Twitter video the Labor leader said it was "democratic." because they wanted to "give up the politics they were elected for".
Eight former former Labor MPs formed a new independent group, and three former Conservative MPs joined their ranks.
Another high-level conservative, Dominic Grieve, said he would quit the party if there were no Brexit without collusion.
The former Attorney General told BBC Newsnight that he admires the courage of the eleven members of the Independent Group and fully agrees with their support for another EU referendum.
He said he could not stay in the Conservative Party if it "got completely out of joint" and backed out of the EU without a negotiating agreement.
Other Labor MEPs have said that they will reflect on their future, unless Mr Corbyn hears their concerns about the Party's culture and acts on them.
While the Labor leader said he was disappointed with the overflows, he suggested the eight were interchangeable, and the Labor movement was "greater than the sum of its parts".
"It is disappointing that some MPs have left our party to sit with dissatisfied Tory MPs, but we can not return to the failed business policy of the past," he said.
"These MPs now want to give up the politics they have been elected for, so it is decent and democratic that they resign and stand for election."
Momentum, the Labor movement based on Corbyn "is to carry out" mass actions "in the constituencies of some former Labor MPs in order to obtain support in the event of a by-election.
She says there will be events Streatham, Stockport and Penistone and Stocksbridge – the constituencies of Chuka Umunna, Ann Coffey and Angela Smith – over the next few weeks.
Labor apology for anti-Semitism
The Labor leader said he would not change direction when he came across the overflows, but reiterated that the fight against anti-Semitism was a priority for him.
He was indicted by Australian MPs, including Joan Ryan and Luciana Berger, who flourished a culture of "anti-Jewish racism" and abused Jews "with impunity" by its supporters.
One of Corbyn's high-ranking team, Barry Gardiner, apologized to the Jewish community in the House of Commons on Wednesday and said he "disappointed" them and Labor "tried" to become "the party we always aspire to . " 
Mr. Corbyn said he acknowledged that the party had sought to restore trust between the Jewish community and persuade people that the party was their "ally" in the fight against anti-Semitism.
"I want to make it absolutely clear that I consider the fight against anti-Semitism an absolute priority and that we are absolutely determined to eradicate anti-Semitism from our party and society.
"Work is the only party deeply rooted in the history of combating racism."
The party said that they have submitted the membership application of the left-wing firefight Derek Hatton on Twitter comments he made about Israel in 2012 exposed.
Lord Mandelson told ITV's Peston that he felt "morally compromised" in "a party that can spit so much hatred t Oward's other members," but he also called on the Labor MPs not to leave the party ,
Conservative defectors insist on "no way back"
Senior Conservatives have suggested that the three Tories who resigned from the party on Wednesday open the door. Anna Soubry, Heidi Allen and Sarah Wollaston will return one day.
Secretary of State Jeremy Hunt said he hoped they would be "welcome" if the government could come back to show Britain remained an open and outward country after Brexit.
Ms. Soubry insisted that there was no "back", as one-nation Tories like them had lost and overpowered the fight for the heart and soul of the party, lmed by a "purple momentum".
And Ms. Allen said she could not imagine returning, "because if we do our jobs right, there will be no Tory party to return to."
She also told the Peston of ITV that "a third" of Tory MPs shared their frustration with the party's direction.
Prime Minister Theresa May has rejected the allegations that the party has abandoned the center of the pursuit of a hard Brexit and pledged to continue offering the "decent, moderate and patriotic policies" that I believe I deserve in the UK
The Times reported that David Cameron, the predecessor of Mrs. May, had staged one last time to convince the three, two of whom were elected in open primaries he advocated.
Mr. Cameron said Twitter, he has respect their decision but did not agree.