Sir Keir said the Prime Minister had “lost control” and MPs would not fall into a “trap” which allowed him to crash Britain out of the EU within weeks.
It comes after Mr Johnson's first defeat as prime minister, where Tory rebels and opposition MPs voted 328 to 301 to take control of business in the House of Commons on Wednesday in a bid to stop a no-deal Brexit.
Mr Johnson leapt to his feet on Tuesday after the crushing defeat to announce he was putting down a motion for a snap election. "The people of this country will have to choose,” he said.
Boris Johnson seeks to trigger snap general election after Commons defeat
A vote on a general election is set to place in the House of Commons this evening but Sir Keir said Labour will not back the move, which would require the support of two-thirds of MPs.
He said: “We are not going to be voting with Johnson today. We are not going to dance to Boris Johnson’s tune... go for an election on a promise from Boris Johnson that it will be on October 15 which we don’t believe.
“We want an election... but we are not going to walk into a trap.”
Asked if it may be preferable to try to form a new government, possibly not with Jeremy Corbyn at the helm, rather than go to the people in an election, Sir Keir added: “It may well be.”
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His aides insisted he was just laying out what could happen under the Fixed Term Act.
Sir Keir also launched a stinging personal attack on the Prime Minister and claimed he might seek to change any agreed election date so it took place after Britain had left the EU.
“He has zero trust because I’m afraid he has been dishonest time and again,” he said. “He’s lied about why he is shutting down Parliament.”
Downing Street and ministers say the prorogation is happening to allow a Queen’s Speech for the Government to press ahead with its domestic priorities — rather than to limit the time MPs have to pass legislation to block a no-deal departure.
A No 10 source added: “Those who state that Parliament is being prevented from dealing with Brexit are being wholly dishonest with the truth, using this to continue their undemocratic plot to stop Brexit altogether.
“Labour have consistently failed to deliver on their promises to the public, frustrating the people’s vote to leave the EU and cowering away from an election they’ve consistently called for so they can attempt to determine the country’s future by their own MPs rather than the people they represent.”
Corbyn and his surrender bill would mean years of uncertainty and delay. I am determined to lead this country forward and take Britain out of the EU on October 31st 🇬🇧— Boris Johnson (@BorisJohnson)September 4, 2019
Business minister Kwasi Kwarteng criticised Mr Corbyn for failing to back a general election and claimed he was “rather frightened” of one. He said it could be “the only way to solve the impasse.”
Sir Keir also said Mr Johnson is "destroying" his own party after withdrawing the whip from 21 Tory rebels, who voted in favour of seizing control of Commons business.
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He told BBC Radio 4's Today programme: "To be honest, removing the whip from well-regarded Tory MPs that have served their party for years amounts to Johnson and Cummings destroying their own party. That will not end well."
The Prime Minister tweeted on Wednesday: "Corbyn and his surrender bill would mean years of uncertainty and delay.
"I am determined to lead this country forward and take Britain out of the EU on October 31st".
The drama also came on a day that Mr Johnson saw his official working majority disappear altogether with the defection of MP Dr Phillip Lee to the Liberal Democrats in protest at Brexit.