Labour MPs who have quit the party should “resign and put themselves up for election”, Jeremy Corbyn has said.
In a Twitter video, the Labour leader said it was the “democratic thing to do” because they wanted to “abandon the policies on which they were elected”.
Eight ex-Labour MPs have formed a new independent group, with three former Conservative MPs joining their ranks.
One of those ex-Tory MPs, Heidi Allen, told ITV’s Peston a third of Tory MPs were fed up with the party’s direction.
Conservative MP Dominic Grieve has said he would quit the party if there was a no-deal Brexit.
The former attorney general told the BBC’s Newsnight he admired the courage of the 11 members of the Independent Group and agreed totally with their support for another EU referendum.
He said he would not be able to stay in the Conservative Party if it “went completely off the rails” and backed leaving the EU without a negotiated agreement.
Other Labour MPs have said they will consider their futures unless Mr Corbyn listens to their concerns about the culture of the party and acts on them.
While the Labour leader said he was disappointed by the defections, he suggested the eight were replaceable and the Labour movement was “greater than the sum of its parts”.
“It is disappointing that some MPs have left our party to sit with disaffected Tory MPs, but we can’t return to the failed business of usual politics of the past,” he said.
“These MPs now want to abandon the policies on which they were elected so the decent and democratic thing for them to do is to resign and put themselves up for election.”
Momentum, the Labour movement backing Mr Corbyn, is to hold “mass canvassing events” in the constituencies of some of those ex-Labour MPs to build support in the event of a by-election.
It says it will have events in Streatham, Stockport, and Penistone and Stocksbridge – the constituencies of Chuka Umunna, Ann Coffey and Angela Smith respectively – in the next few weeks.