MPs will have their say on the next steps for Brexit later after European leaders indicated they would consider delaying the UK's departure if a deal is not agreed by 29 March.
Germany's Angela Merkel said if the UK needed more time to get Parliament's approval, she would "not oppose" it.
Theresa May has said MPs will get a vote on delaying Brexit if her deal and a no-deal outcome are both rejected.
MPs will vote on amendments to a government motion in the Commons later.
Wednesday's votes are not on Mrs May's Brexit deal itself - she says that will happen before 12 March.
Instead, MPs are seeking assurances and to hold the PM to her commitment, made on Tuesday, to allow MPs a vote on extending 29 March's Brexit deadline to avoid Britain leaving without a deal.
The prime minister's critics have accused her of "kicking the can down the road" with her pledge to hold more votes before 12 March - just 17 days before Brexit.
But she insisted her efforts to persuade the EU to make concessions had "already begun to bear fruit".
The government has accepted an amendment by Conservative MP Alberto Costa, which seeks to protect the rights of UK citizens in the EU, and vice versa, regardless of the outcome of UK-EU negotiations.
The amendment - which calls on the UK to secure agreement on this at "the earliest opportunity" - had gained significant cross-party backing from 141 MPs - including Labour and the Democratic Unionists.
Despite this, Mr Costa has resigned his job as aide to Scottish Secretary David Mundell, because, he told MPs, of a convention that members of the government should not amend government motions.
He said he "welcomed" the government's support for his amendment but it did not go far enough.
He said he wanted ministers to spell out "exactly what measures" Theresa May will now take to guarantee citizens rights and urged her to write to European Council President Donald Tusk.
He said the rights of the estimated million UK citizens living in the EU, and the three million EU citizens in the UK, "should never have been used as a bargaining chip" in the government's Brexit negotiations.
Green MP Caroline Lucas praised Mr Costa's stand and called for him to be reinstated in the government.
Analysis by Nick Eardley, BBC Political Correspondent
It looks a bit strange, doesn't it?
The government accepts an amendment from a member of the government - but then essentially sacks that member of the government for tabling it in the first place.
I'm told by several people that Alberto Costa was left with no decision but to resign. He met with the prime minister this morning made it clear he wasn't backing down which sealed his fate.
That's left some Tories furious. They point out he has a personal interest in the EU citizens' rights issue given his Italian parentage and say he was simply trying to get assurances he had been offered by Theresa May backed by the Commons. One member of the government said the treatment of Mr Costa had been appalling.
But a senior ally of the PM says Mrs May was left with no choice. It is, they point out, against the rules for members of the government to table amendments to government motions. This is a clear black and white example of breaking, they conclude, unlike some recent comments from cabinet ministers which could be open to interpretation (again their argument, not mine).
Another junior member of the government says that if Mr Costa had moved his amendment as a member of the government tonight - and it had been passed - it would have set a terrible precedent and led to many more similar situations.
Five amendments - out of 12 originally tabled - were selected for debate by Speaker John Bercow.
The Labour leadership's amendment calls on MPs to support its alternative Brexit plan, which would include a "comprehensive customs union" and close alignment with the EU in the future.
If that proposal is voted down, Jeremy Corbyn has said the party would move to formally back another EU referendum "in order to prevent a damaging Tory Brexit" or no-deal outcome.
Mrs May has accused Labour of "playing political games" and argued the best way for the country to move forward is for MPs to approve the revised deal she hopes to bring back.
The SNP amendment insists the UK should not leave the EU in any circumstances without a deal "regardless of any exit date".
On Tuesday, Theresa May promised MPs a vote on delaying Brexit for a short period if MPs reject her deal and leaving without a deal.
This was designed to head off a potential defeat on a cross-party amendment tabled by Labour MP Yvette Cooper, which calls for the same thing.
Ms Cooper has not withdrawn her amendment, because she wants to hold the prime minister to her commitment.
She said: "We will keep up the pressure working cross-party to ensure the commitments are implemented... to avoid any backsliding and to make sure we do not end up with a chaotic no deal."
An amendment by Conservative MP Dame Caroline Spelman and Labour's Jack Dromey amendment - calling for Parliamentary time to make the PM's no-deal vote commitment legally binding - will not be put to the vote, following government assurances.
"The government has just confirmed acceptance of all the proposals in our amendments. There will not now be a no-deal Brexit In 30 days' time because there is not a majority in the House for crashing out without a deal," the MPs said in a joint statement.
What does it mean to table an amendment?
The process starts with the government putting down a motion. It is a plain piece of text, asking the House to note the prime minister's most recent Brexit statement - made on Tuesday - and that discussions between the UK and the EU are ongoing.
This then allows MPs to table amendments - alternative options - to that motion, setting out their proposals on what they think should happen next.
Mrs May said any delay to the UK's departure should not go beyond the end of June and "would almost certainly have to be a one-off".
Extending Article 50 would require the unanimous backing of the other 27 EU member states - something they have indicated they would be happy to do.
Speaking on Wednesday, German Chancellor Angela Merkel said she would "not oppose" a request from the UK for more time although French President Emmanuel Macron struck a more sceptical note, saying there had to be a "clear objective" behind any extension.
"As our negotiator Michel Barnier has said, we don't need more time but decisions," he said during a meeting in Paris. "The time has come therefore for the British to make choices."