The government has insisted it will not allow MPs to tie its hands in Brexit negotiations, despite being forced to offer a last-ditch concession to Tory rebels to stave off a House of Commons defeat.
MPs will hold further votes on the EU Withdrawal Bill later, including on a House of Lords demand for the UK to remain in the EU's single market.
On the return of the EU Withdrawal Bill for consideration by MPs on Tuesday, the government won all the day's votes as it overturned a series of House of Lords amendments to the key Brexit legislation.
However, a potential rebellion by pro-Remain Tories over their demands for a "meaningful vote" on the final Brexit deal was only avoided after ministers agreed at the last moment to discuss a compromise.
They subsequently warned they will not be easily bought off in talks to come, while Tory Brexiteers urged ministers not to concede any ground.
During a frantic day of discussions between ministers and Conservative backbenchers, potential rebels were eventually persuaded to back down when Solicitor General Robert Buckland told MPs that ministers were willing to "engage positively" with their concerns.
Talks will now be held between ministers and Tory MPs uneasy with the government's handling of Brexit, in the hope of reaching an agreement before the legislation is passed back to the House of Lords.
A group of backbenchers had been planning to back an alternative amendment spearheaded by former attorney general Dominic Grieve, which would have given MPs a greater say over the Brexit process.
This included the House of Commons having to approve any government action in Brexit talks if it has not reached an exit deal with the EU by the end of November.
Mr Grieve told Sky News he had received "assurances" from Theresa May in a meeting on Tuesday afternoon that the MPs' concerns would be addressed.
This led him not to force his own amendment to a vote, while the potential rebels backed away from voting against the government on a similar House of Lords amendment, thereby allowing ministers to remove the peers' changes to the bill.
"We had a personal assurance that we would find a way of addressing the concerns which are encapsulated in these amendments," Mr Grieve said as voting continued on Tuesday.
"We will be talking to the government immediately after this in order to find a common way forward. I'm fairly confident we will be able to do that."
However, despite backing down, pro-Remain Tories signalled they would not be easily consoled by a compromise offered by ministers.
Sarah Wollaston warned that any government amendment added to the bill when it returns to the House of Lords "must closely reflect Dominic Grieve's amendment".
Her fellow Conservative backbencher Stephen Hammond said: "Parliament must be able to have its say in a 'no deal' situation.
"The government have conceded that this is necessary and I expect to see a new amendment to cover this situation soon."
Heidi Allen later warned the prime minister against reversing on her promise, telling Sky News: "When it [the bill] comes back, if it's not improved, we will vote against the government."
Earlier, the prime minister had been hit by the resignation of justice minister Phillip Lee, who came out in support of a second referendum on the UK's final divorce deal and criticised Mrs May's Brexit policy.
Commenting after Tuesday's votes, Dr Lee said: "Delighted that the government has agreed to introduce an amendment to the EU Withdrawal Bill which will give parliament the voice I always wanted it to have in the Brexit process.
"This justifies my decision to resign and makes it a lot less painful."
Fellow Tory Remainers Anna Soubry and Ken Clarke were not convinced by ministers' concession and voted against the government by backing the Lords amendment on a "meaningful vote".
During Tuesday's debate, Ms Soubry told the House of Commons that a fellow Remainer MP had to be guarded by six armed undercover police officers at a recent public event.
Although their compromise offer bought off other potential Tory rebels, the government later issued a series of red lines they would not cross in trying to appease backbenchers.
Mr Buckland told Sky News: "What I won't accept is some sort of mechanism to tries to mandate or direct the government to do things because I think that not only is that constitutionally suspect but it actually weakens potentially the government's negotiating position."
Meanwhile, Tory Brexiteer Bernard Jenkin told the government he would not accept ministers agreeing to Mr Grieve's demand for the House of Commons to assume control of Brexit negotiations in the event of no deal.
Dismissing claims that Mrs May had effectively abandoned her threat that the UK could leave the EU without a deal, Mr Jenkin said: "There is only agreement for discussions, not concessions."
His fellow Brexiteer, Jacob Rees-Mogg, claimed Mr Grieve's demand for parliament to assume control of the Brexit process "inevitably makes leaving without a deal more likely because it's so inflexible".
The tensions among Conservatives will see frantic efforts by Mrs May to appease both Leave and Remain sides of her party.
There is also the potential for another crunch vote in the House of Commons next week.
Commenting on the government's actions to avoid a defeat over the "meaningful vote" demands, Labour's shadow Brexit secretary Sir Keir Starmer said: "Facing the prospect of a humiliating defeat, Theresa May has been forced to enter negotiations with her backbenchers and offer a so-called concession.
"We will wait and see the details of this concession and will hold ministers to account to ensure it lives up to the promises they have made to parliament."