Official party social media accounts trumpeted the prime minister's second reading victory on Tuesday night with a string of posts, which also accused Labour of voting to delay Brexit.
But critics pointed out the Withdrawal Agreement Bill (WAB) only passed its first Commons hurdle - known as second reading - before the prime minister paused the legislative process.
It still needs to pass several Commons and Lords stages before it can become law, leaving the legislation vulnerable to amendments from opposition MPs.
Former Tory minister Sam Gyimah, now a Liberal Democrat, said: “Fake news alert. Conservatives claiming their Brexit deal has passed parliament is like the England team saying they’ve won the World Cup, when they’ve just qualified for the knock-out stages.
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"Yet again they are playing the electorate for fools.”
Ex-Tory chancellor George Osborne, who edits the Evening Standard, also waded into the row after his newspaper ran a story accusing his old party of misleading the public.
He tweeted: “I think you’ll find the team at the Evening Standard know the difference between a bill passing its second reading in the Commons and a bill passing parliament.
“I know it’s been a while since the latter happened, but I’m happy to come in and explain how it’s done.”
Labour's Valerie Vaz raised concerns about the party's social media posts in parliament with Jacob Rees-Mogg.
She said: "There is an outrageous tweet going around, and I would like the leader of the House to confirm this. It's on the official Conservative Party account claiming that the deal has passed parliament and calling for donations."
She added: "The deal has not passed the House, it has passed its second reading but we on this side stand ready to provide consensus on a programme motion that will look at proper scrutiny."
Mr Rees-Mogg, the Commons leader, replied: "The question of the Conservative Party website falls outside my formal remit but the deal has passed its second reading.
"That is a passage through parliament, that is an indication of parliament's assent. It is not, however, an indication of the complete legislative programme. I don't think that's an unduly difficult concept."
A Conservative Party spokesperson said: "MPs have passed the new deal that the prime minister negotiated with the EU at second reading, but sadly parliament and Jeremy Corbyn are still delaying actually getting Brexit done once and for all.
"Only the Conservatives are committed to getting Brexit done so we can focus on domestic priorities like more police on the streets and investing in the NHS, and finally allowing the country to move on.”
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