The UK's highest court ruled Johnson's decision to suspend Parliament was unlawful - prompting opposition calls for him to resign, the BBC reported.
The PM was forced to cut short his visit to the UN in New York to explain his legal defeat to the Commons.
Jeremy Corbyn said he should "have done the honourable thing and resigned".
But Johnson goaded the Labour leader and other opposition parties to "finally face the day of reckoning with the voters" in a general election.
Labour and the SNP have refused to do that until a no-deal Brexit has been taken off the table.
Johnson said: "I think the people outside this House understand what is happening.
"Out of sheer selfishness and political cowardice they are unwilling to move aside and let the people have a say. The Leader of the Opposition and his party don't trust the people.
"All that matters to them is an obsessive desire to overturn the referendum result."
He said Labour had "until the House rises today to table a motion of no confidence in the government, and we can have that vote on Thursday".
"Or if any of the other smaller parties fancy a go, table the motion, we'll give you time for that vote.
"Will they have the courage to act, or will they refuse to take responsibility yet again and do nothing but delay?"
Under the Fixed Terms Parliament Act, the Prime Minister cannot call an election unless two-thirds of MPs back it.
But a motion of no confidence in the government only needs a majority of one.
Labour has said it does not trust to Mr Johnson to obey Parliament's instructions to request a delay to Brexit, which the PM has insisted will happen on 31 October, with or without a deal.
Corbyn told MPs: "Quite simply, for the good of this country, he should go.
"He says he wants a general election. I want a general election. It's very simple - if you want an election, get an extension and let's have an election."
The government is under no obligation to give time to any call for a motion of confidence from anyone other than the leader of the opposition.
It is unprecedented for the government to voluntarily offer time to the opposition and smaller parties to debate such a motion.
Attorney General Geoffrey Cox earlier faced questions about the advice he gave the PM indicating the five-week suspension would be within the law.
Cox said he respected the Supreme Court's decision, but launched a blistering attack on MPs for being "too cowardly" to hold an election, adding: "This Parliament is dead."
The Attorney General was branded a "disgrace" by one MP, while another said he was "horrified" at his language, in angry scenes.
The SNP's Joanna Cherry - who was one of the lawyers who led the court challenge against the suspension or "prorogation" - said Cox was being "offered up as a fall guy for the government's plans" and urged him to publish the advice he gave.
( With inputs from IANS )