May said parliament would debate the deal in January, before a vote in the week beginning Jan. 14 - more than a month after an original December 11 vote which May cancelled after admitting she faced a significant defeat.
Additionally is not the same as a formal no confidence vote, which would trigger a general election 14 days after being defeated.
According to reports, Corbyn was to propose: "That this House has no confidence in the Prime Minister due to her failure to allow the House of Commons to have a meaningful vote straight away on the withdrawal agreement and framework for the future relationship between the United Kingdom and the European Union".
British Defense Secretary says around 3,500 troops will be on standby in support of the government to help deal with any disruptions in the event of a "no-deal" Brexit.
May is trying to persuade European Union leaders to sweeten the Brexit deal, after she pulled a planned parliamentary vote in the face of anger in her own Conservative party.
Parliament broke up for a 17-day Christmas recess, without deciding whether to approve the government's divorce deal with the European Union.
May's cabinet is divided between ministers who want the government to embrace a no-deal outcome and those who favour parliament having a final say in a series of votes on potential scenarios for Brexit.
Rees-Mogg led a party confidence vote against May last week, which she survived, but only after a third of her parliamentary party voted to oust her.
"That's why we have been doing a lot of work in relation to, for example, the Channel ports, why we have issued 106 technical notices now, why we are recruiting another 300 people for Border Force".
In a warning to campaigners calling for a second referendum, she said it would "break faith with the British people" and do "irreparable damage to the integrity of our politics".
"Another vote which would likely leave us no further forward than the last".
Theresa May, who will chair the JMC meeting, said: "I am confident that what we have agreed delivers for the whole of the UK".
She backed the idea of an indicative vote so MPs could reveal which options they would back if Mrs May's deal cannot get through.
With less than four months before Britain is due to leave in March, Brexit, the biggest shift in trade and foreign policy for more than 40 years, is proving anything but smooth, complicated by the deep divisions in parliament and across the country.
The SNP's Ian Blackford, who signed the amendment, said: "It is clear the Prime Minister's tactic has been to run down the clock and deprive Parliament of any alternative to her deal. Not only do we need to prepare the country, but it's also the best way that we will ensure that we get a deal".
The PM's key aides - her chief of staff Gavin Barwell and de facto deputy PM David Lidington - were accused of exploring the possibility of a "People's Vote" to break the Brexit deadlock, The Sun reports.
Downing Street said that advice on no-deal preparations will be going out to households by various channels over the coming weeks.
Labour insisted it was clearly a confidence motion and should be allocated time for debate by the Government.
But as she emerged from Number 10, Ms Sturgeon restated the Scottish National Party's determination to vote against the deal when it returns to the Commons in January.