Following the decision of seven Labour MPs to walk out on Monday, colleagues expressed anger with the leadership during a “tense” meeting in Parliament.
Corbyn-critic Ian Austin said others would “think hard” about leaving unless it fixed its anti-Semitism problem.
The BBC has been told two Tory MPs are thinking about joining the ex-Labour MPs’ independent group in Parliament.
The BBC’s political editor Laura Kuenssberg said a small number of Conservatives were considering their futures amid unhappiness over the government’s Brexit policy.
Chuka Umunna, Luciana Berger, Chris Leslie, Angela Smith, Mike Gapes, Gavin Shuker and Ann Coffey quit Labour’s ranks in protest at what they said was a culture of “bullying and bigotry” in the party and frustration over the leadership’s reluctance to back another EU referendum.
The seven are not launching a new political party but have urged other Labour MPs – and members of other parties – to join them in “building a new politics”.
Their departures have provoked a mixed reaction at the top of the party, with Shadow Chancellor John McDonnell saying they should stand down and allow by-elections in their constituencies.
But deputy leader Tom Watson said the move was a wake-up call for the party. He condemned those on the “hard left” who he said were celebrating their exit, saying he “sometimes no longer recognised” the party.
Edinburgh South MP Ian Murray told the BBC he was sticking with Labour but “may change his mind” unless the party responded to concerns about its culture and direction.
Speaking after a Labour meeting in Westminster – addressed by party chairman Ian Lavery – Mr Austin said Labour must act to stop more MPs jumping ship.
Mr Austin said Mr Lavery had failed to “demonstrate the leadership” and “understand the scale of the problem we have” with anti-Semitism within its ranks.
“If that is the best the leadership can do, I can see more people taking the same course of action,” he said.
“I think it will result in people thinking long and hard about their position in the party.”
The BBC’s political correspondent Ben Wright said several MPs thought Mr Lavery had misjudged the mood of the meeting by delivering a tub-thumping speech about being proud of the party.
But he said he did not get a sense that other MPs were poised to join the splinter group.
Party sources said Mr Lavery had insisted Labour must remain a “broad church” and it was determined to root out the “appalling abuse” that Ms Berger in particular had been subjected to.
Announcing her resignation on Monday, the Liverpool Wavertree MP said Labour had become institutionally anti-Semitic and she was “embarrassed and ashamed” to stay.
Meanwhile, Ms Coffey – one of the seven who quit – was asked on BBC Breakfast about whether more MPs could follow her.
“A number of my colleagues have expressed concern privately, but everybody has their own journey and it’s a huge thing to do to leave and resign from a party,” she said.
Labour MP Jess Phillips, writing in the Daily Telegraph, called on Mr Corbyn to listen to why the MPs had quit and “act on it”, warning that reacting with bitterness could cause the party to “burst apart”.
However, shadow foreign secretary Emily Thornberry told the Daily Mirror that the resignations were a “distracting and divisive exercise”.
A new political landscape?
So far they are not a political party, although they say they may evolve into one. So far they have no leader, and no policy programme as such.
They are clearly open to welcoming disgruntled members of the Conservative Party too.
Their view is that our whole political system is broken and neither the Tories nor Labour are fit for purpose. And it is possible that within days they might be joined by a sprinkling of Tory MPs.
This splintering might, just might – in time – turn into a much bigger redrawing of the landscape.
For now though that is way off. And this is first and foremost about the Labour Party – the seeds of the splinter sown more than three years ago, bearing bitter fruit just when Parliament’s biggest decisions over Brexit are about to be made.
In a founding statement on its website, the group sets out its approach to the economy, public services and security, as well as Brexit.
But the seven MPs rejected comparisons with the SDP which broke away from the Labour Party in the early 1980s and eventually merged with the Liberal Party.
Mr Corbyn said he was “disappointed” the MPs had felt unable to continue working for the policies that “inspired millions” at the 2017 election.
The Labour leader is likely to be pressed on the issue when he makes a speech on Brexit and education on Tuesday – in which he will announce the setting up of a new commission on life-long learning.
Mr Corbyn is also likely to face questions after Derek Hatton – the face of the hard-left Militant Tendency group in the 1980s – said he had rejoined the Labour Party.
Mr Hatton, who was expelled from Labour in 1986, told the BBC that his membership had been approved although Labour said it could not comment on individual applications.
Mr Hatton, 71, told BBC Radio 4’s Today programme “it’s good to be back”, adding: “In a way I’ve never left. For 34 years I have stayed absolutely solid with the Labour Party.”
Commenting on the seven MPs who left, he said: “How pathetic, how really strong are you within the Labour movement to want to run away when there’s something you disagree with?”
Meanwhile, Brexit Secretary Stephen Barclay is to brief the Cabinet on his latest negotiations with the European Union.
The Department for Exiting the EU said he had a “productive” discussion with the EU’s chief negotiator Michel Barnier in Brussels on Monday.