But speaking in Downing Street with the sound of protesters threatening to drown him out, Johnson said: "I don't want an election, you don't want an election."
On the possibility of a deal with the EU to allow Britain's orderly departure, he said he was "encouraged by the progress we are making" but that under no circumstances will he ask Brussels for a delay to the October 31 deadline.
He had earlier called an unscheduled cabinet meeting in the face of a potential revolt from some of his own Conservative members of parliament.
Some Conservatives joined opposition parties in angrily reacting to Johnson's decision last week to suspend parliament from mid-September to mid-October in order to introduce a new legislative programme, limiting the number of parliamentary sittings in the next two months, which prompted thousands to take to the streets on Saturday.
Some of his own party's lawmakers say it was a ruse to limit parliament's options to stop no deal and are willing to vote with the opposition to try to prevent that outcome - even if it leads to a confidence vote that could ultimately bring down the government, which has a tiny majority.
Opponents fear no deal could do enormous economic damage to Britain.
But Johnson believes another delay to Brexit, which was due to happen at the end of March, would be undemocratic and says those frustrating the process simply want to block Brexit altogether and go against the country's 2016 referendum result.
According to media reports, the surprise deliberations in cabinet focused on how the government should handle a possible defeat this week in parliament, which returns to work on Tuesday after a summer recess.
Opponents of a no-deal Brexit from across parliament want to legally compel Johnson to seek a postponement of Britain's date to leave the EU, should there be no withdrawal agreement with Brussels.
According to media reports, they want to postpone the Brexit date by three months, to January 31, unless a deal is reached by October 19.
Tory parliamentary leaders said lawmakers who support attempts to block a no-deal Brexit will not be allowed to run for the party in the next general election. They would also be expelled from the party's ranks in parliament and considered independents.
"They seem to be quite prepared for there to be a rebellion, then to purge those who support the rebellion from the party," Conservative no-deal opponent David Gauke told BBC radio.
Johnson says he is attempting to force the EU to make concessions by threatening a no-deal Brexit. He wants to renegotiate an existing withdrawal deal to remove the so-called backstop clause that guarantees an open border remains between the Republic of Ireland and Northern Ireland after Brexit.
Johnson, who succeeded Theresa May in July after her deal with the EU was continually rejected by parliament, wants an open border but believes the current deal would leave Britain trapped.
Brussels has refused to remove the backstop from the withdrawal agreement and called - in vain - on Johnson to specify exactly what his alternative solution might be. An EU Commission spokeswoman said Monday that there were no new developments.
British Education Secretary Gavin Williamson told Sky News: "We all got elected in 2017 on a clear manifesto commitment to deliver Britain's exit from the EU.
"And by voting with Jeremy Corbyn and the Labour opposition all you're doing is weakening the prime minister and Britain's hand in order to deliver Britain's exit with a good deal."
Corbyn, opposition Labour Party leader, pledged in a speech that his party was "working with other parties to do everything necessary to pull our country back from the brink. Then we need a general election."
The government has meanwhile launched a multimedia information campaign, "Get ready for Brexit," for businesses and people on how to prepare.
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