Labour leader Jeremy Corbyn has stepped up calls for a general election "at the earliest opportunity" to "break the deadlock" over Brexit.
In a speech, he said a new government would have a fresh mandate to negotiate a better withdrawal deal with the EU.
He told Theresa May: "If you are so confident in your deal, call that election, and let the people decide."
The Conservatives said Labour did not have a plan for Brexit and were "playing politics".
Mr Corbyn has resisted growing calls from within his own party to get behind another EU referendum, insisting an election is still his top priority if Theresa May's Brexit deal is rejected by MPs next week.
The UK is set to leave the European Union on 29 March. The withdrawal agreement between the UK and EU - covering things like trade, expat citizens' rights and setting up a 20-month transition period - will only come into force if MPs back it in a vote.
Labour is set to vote against Mrs May's deal next Tuesday and if, as widely expected, it is defeated, they are expected to start moves to trigger a general election.
Asked if this would happen immediately, Mr Corbyn said Labour would "table a motion of no confidence in the government at the moment we judge it to have the best chance of success".
If a majority of MPs back a no confidence motion, the government will get 14 days to try and win another confidence vote - if it can't do that, a general election will be held.
Mr Corbyn said: "Clearly, Labour does not have enough MPs in parliament to win a confidence vote on its own. So members across the House should vote with us to break the deadlock."
Northern Ireland's Democratic Unionist Party, which is also against Mrs May's deal, has said it will back her in any confidence vote.
As debate on the Brexit deal resumed in the House of Commons for the second of five days, it emerged that some of Mr Corbyn's Leave-supporting backbench MPs have been speaking to Theresa May about backing her deal if she can guarantee environmental standards and rights for workers.
But Mr Corbyn said Labour did not "endorse or accept" a reported offer from the government to adopt an amendment to protect workplace and environmental rights.
"It's already been quite clearly and emphatically rejected by the TUC and leading trade unions. They say it simply doesn't guarantee the protections that we are seeking."
Theresa May has, meanwhile, reached out to union leaders to seek their backing for her deal, it has emerged.
The prime minister made telephone calls to Len McCluskey, general secretary of Labour's biggest financial backer Unite, and GMB leader Tim Roache.
Mr Roache said: "As you would expect, I was very clear about GMB's position - the deal on the table isn't good enough and non-binding assurances on workers' rights won't cut it."
Labour MPs on the anti-Brexit side of the party are calling on Mr Corbyn to get behind the campaign for a new EU referendum - something polls suggest is supported by the majority of Labour members.
Mr Corbyn has said his preferred option is to trigger a general election and, having won it, seek to delay Brexit in order to negotiate a better deal with Brussels, which he says would see the UK in a permanent customs union with the EU and with a close relationship with the single market.
This policy, together with a "radical" Labour government would kick start economic growth, and "allow a renaissance in our manufacturing sector, which will create good, secure jobs and help restore pride and prosperity to parts of our country that have been ignored for too long", he argued.
If Labour is not able to get a general election, Mr Corbyn said all options were "on the table, including the option of campaigning for a public vote".
Asked if a fresh referendum would be in Labour's election manifesto, he said: "Our policy would be to negotiate urgently with the EU as and when we take office, but clearly a general election must come first in order to do that.
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"Policy-making is made by the Labour Party in a democratic form and that policy will be put together and put into a manifesto in any election that's coming up."
He said he understood the concerns of younger voters, who polls suggest overwhelmingly backed another referendum on staying in the EU, but he also understood those who had voted to leave the EU and he wanted to bring the country together.
In a speech to Labour activists at an electrical products manufacturer in Wakefield, West Yorkshire, Mr Corbyn said Theresa May would forfeit the right to govern if she cannot get her Brexit deal through the Commons.
"A government that cannot get its business through the Commons is no government at all. It has lost its mandate so must go to the country to seek another."
Mr Corbyn vowed to heal the divide between Leave and Remain voters, saying the "real divide" in the UK was between the "many" who "do the work, create the wealth and pay taxes" and the "few" who "set the rules, reap the rewards and so often dodge taxes".
He said: "The real solution is to transform Britain to work in the interests of the vast majority, by challenging the entrenched power of a privileged elite.
"That is how we can help to heal the referendum's deep divisions."
Conservative Party chairman Brandon Lewis, said: "Labour simply do not have a plan for Brexit. Instead they are arguing in public about whether to frustrate the decision of the British people and rerun the referendum."
The cross-party People's Vote campaign for another referendum, which is backed by about 30 Labour MPs, also criticised Mr Corbyn's speech.
Campaign supporter and Green MEP Molly Scott Cato said: "Many Labour MPs, not to mention the party's voters and members, will be horrified by the prospect that their party leader is still proposing to fight the next election as a supporter of Brexit."
Plaid Cymru MP Jonathan Edwards, another People's Vote supporter, said: "An election in which both Labour and Conservative Brexit policies are almost indistinguishable will solve nothing."