Mr Johnson was earlier called “racist” and “not fit for office” during PMQs by Ian Blackford, the SNP leader in the Commons.
Senior Labour MPs put pressure on leader Jeremy Corbyn to back a second Brexit referendum at a shadow cabinet meeting.
Nigel Farage, meanwhile, claimed the Brexit Party could form an electoral pact with a Johnson-led Conservative Party to deliver a no deal exit.
See how the day unfolded below:
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Welcome to The Independent's live coverage of the third round in the Tory leadership race.
Last night's vote saw Dominic Raab forced out, leaving Boris Johnson, Jeremy Hunt, Michael Gove, Rory Stewart and Sajid Javid still in the running.
The first debate involving frontrunner Mr Johnson last night is unlikely to have swayed many MPs' minds, ending with no clear winner after a fractious debate taking in Brexit, Islamophobia, tax cuts and climate change.
However, Michael Gove claimed he "won the debate" on BBC Newsnight, "because I had the most detailed answers and I have a clear plan to how we can deliver Brexit and make sure we get all the benefits of life outside the European Union".
Adam Forrest has covered the five key Boris Johnson moments from last night's debate:
As the candidate who currently has the fewest number of backers, there are rumours Sajid Javid could drop out, but supporter Stephen Crabb MP told Newsnight his favourite had performed well in the debates and was not about to quit.
"Did Sajid Javid look like a man who's about to throw in the towel or about to be knocked out of the contest?" Mr Crabb said.
"He fought tonight, I thought he gave - in a difficult format - he gave a good display of what he can offer the country."
During the BBC debate, Mr Johnson's rivals had turned on him over his ambition to give people earning more than £50,000 a tax cut. He was also taken to task over his comments comparing veiled Muslim women to "letterboxes" and "bank robbers". Adam Forrest covered the debate:
Nigel Farage has said he would be willing to form a pact with Mr Johnson to deliver a no-deal Brexit, Rob Merrick writes:
Also during last night's debate, Mr Johnson said he would lift the National Insurance threshold for the low-paid, but there should be a "debate" about the 40p higher income tax rate, which currently kicks in at £50,000.
"It does seem to be very odd that in the Conservative Party people should seriously question whether it is right to try to lift nurses and heads of maths departments and police inspectors out of the top rate of tax," he said.
Andrew Woodcock has the story:
The candidates also clashed over Brexit:
- Mr Stewart insisted Theresa May's Withdrawal Agreement was the only route out of the European Union, while "everybody else is staring at the wall shouting 'Believe in Britain'."
- Mr Gove said the Withdrawal Agreement had already been rejected three times and "you cannot simply re-present the same cold porridge for a fourth time and ask people to say that's what they want".
- Mr Johnson said the 31 October deadline for leaving the EU must be met "otherwise, I'm afraid, we face a catastrophic loss of confidence in politics".
- Mr Javid said it had been a "mistake" to have a flexible deadline, and the 31 October date would concentrate minds on both sides of the Brexit negotiations.
-Mr Hunt said he would delay beyond 31 October if a deal was in reach, as "if we were nearly there, then I would take a bit longer", a point echoed by Mr Gove, who said he would allow "extra time" to be played to secure an agreement.
Adam Forest has more:
In yesterday's ballot, Mr Johnson built on his lead to secure 126 votes - 12 more than the first round - putting him 80 ahead of Mr Hunt who had 46 votes, up three.
Mr Gove put on four votes to reach 41, while Mr Stewart surged into fourth place on 37, gaining 18 votes since last week.
Mr Javid scraped into the next stage of the contest, just meeting the threshold of 33 votes - a gain of 10 - while Mr Raab was eliminated with 30 votes.
Andrew Woodcock has more:
Mr Stewart said he has received positive responses from backers of eliminated hardline Brexiteer candidate Dominic Raab.
The international development secretary told BBC Radio 4's Today programme: "I have had some positive responses, yes. I had a couple this morning."
Referring to his stance on Brexit, Mr Stewart said: "The reason for that [support] is that like me, they feel - and, I feel, like Dom - that we have to get this done."
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