But Solicitor General Robert Buckland said while talks may "yield fruit" - he could not guarantee a change in policy.
"The main reason for my taking this decision now is the Brexit process and the government's wish to limit parliament's role in contributing to the final outcome in a vote that takes place today", he said in a statement released on his website. That supposedly, according to BBC's Political Editor Laura Kuenssberg, drew a colorful response from a pro-EU Tory rebel: "If she f**ks us, she's f**ked".
Rebels have said they will challenge May's plans to leave the customs union during votes on other bills, on trade and customs, which will be brought back to the house some time before July 24.
Due to the concessions offered, the details of which have not yet been fully revealed, two Conservative MPs - Ken Clarke and Anna Soubry - rebelled.
The concession on a meaningful vote came after intensive horse-trading on the floor of the House of Commons, with chief whip Julian Smith shuttling between Tory backbenchers during debate on Lords amendments to the EU Withdrawal Bill.More news: South Korea Blindsided By Trump War Games Agreement
Former Attorney General Dominic Grieve had been a repeat rebel in previous debates, but he voted with the government after "personal assurances" from Theresa May - because he is "quite satisfied" MPs will end up with a meaningful vote anyway.
Although these terms would not necessarily keep the United Kingdom in the customs union, defeat in the Commons would be politically explosive, as it would show May has no majority for one of her key "red lines".
Politics is often about the big picture, but sometimes it is a festival for pedants.
Passions ran high in Tuesday's three-hour debate, when angry eurosceptics accused their rivals of trying to undermine the 2016 referendum vote to leave the EU. "We must think about the message parliament will send to the European Union this week", Ms. May's preferred approach is temporarily keeping the U.K.in some form of temporary customs union with the E.U., but this is unacceptable to hardline Brexiteers in her party.
"I trust the prime minister. I'm fairly confident we will be able to do that".More news: Maria Bueno, Brazilian Tennis Star, Dies Aged 78 Following Cancer Fight
May is resisting changes approved by the House of Lords that would soften Britain's exit from the European Union, because she says they will weaken the government's negotiating position.
Mr Grieve withdrew his own amendment, which would have given MPs powers to dictate what the Government should do if no acceptable agreement is reached by February 2019.
"We have not, and will not, agree to the House of Commons binding the government's hands in the negotiations".
He rejected suggestions ministers were already backtracking on promises made to MPs, insisting he did not want to raise any "false expectations". "It is clear we don't just want to have a chat but a proper discussion and negotiation".
The government was putting a combative spin on the concessions Tuesday evening: "The Brexit Secretary has set out three tests that any new amendment has to meet - not undermining the negotiations, not changing the constitutional role of Parliament and Government in negotiating worldwide treaties, and respecting the referendum result", a spokesperson for the Brexit department said in a statement.More news: Tesla laying off 9 percent of workforce
Earlier May suffered a setback when junior justice minister Phillip Lee, who has always been critical of Brexit strategy, resigned and said he would vote against the government.
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