BRUSSELS -- European Union chief Brexit negotiator Michel Barnier said Wednesday there will be "no turning back" for Britain on commitments made during an initial divorce deal between the two, after his U.K. counterpart insisted it was merely a "statement of intent."

Barnier told legislators at the European Parliament that the negotiations so far have been "extremely complex and extraordinary" but insisted that he had made no concessions to the British side.

U.K. negotiator David Davis suggested over the weekend that the deal was less than cast in stone. But Barnier said "progress has been noted and recorded and is going to have to be translated into a legally binding withdrawal agreement" on the EU bill Britain faces, the maintenance of a transparent border between EU member Ireland and the U.K.'s Northern Ireland, and citizens' rights in each other's region.

The European Parliament's chief Brexit official, Guy Verhofstadt, said Davis was already backtracking after his statement Sunday, which riled officials in Brussels.

Verhofstadt said he and Davis had spoken by phone on Tuesday and that Davis "assured me it is absolutely not his intention, not the intention of the U.K. government, to backtrack on their commitments.

"The best way to secure this is that in the coming weeks we transpose all these commitments into the legal text of a withdrawal agreement," he said.

Most of the legislature had warm words for the performance of Barnier in running a tight ship during the talks and keeping the 27 remaining EU nations united in their stance.

EU leaders open a two-day summit on Thursday during which they are slated to agree that there has been "sufficient progress" for the talks to move to the second phase of future relations and trade, a subject Britain wants to open as soon as possible.

Britain is due to leave the bloc in March 2019, but a Brexit deal will have to be agreed by the fall of 2018 to give national parliaments time to approve it.

European Union Council President Donald Tusk warned Tuesday that it would be a "furious race against time" to finish Brexit negotiations by autumn, saying only "moderate progress" has been achieved so far.

Meanwhile, British Prime Minister Theresa May was scrambling to stave off defeat on its key Brexit bill from lawmakers demanding a greater say over the decision.

The House of Commons is due to vote Wednesday on a motion insisting a deal with the EU require an Act of Parliament before it can take effect.

May's Conservative government lacks an overall majority, so it would only take a few Conservative rebels to join the opposition to deliver defeat.

Brexit Secretary David Davis has written to Conservative lawmakers, promising the government will not implement a Brexit deal without Parliament's approval.

It's unclear whether the government has done enough to avoid a defeat that would damage May's already precarious authority.

The vote comes as an amendment to the EU Withdrawal Bill, which is making its way through Parliament.

The bill forms the legal scaffolding for Brexit, converting some 12,000 EU laws into British statute on the day the U.K. leaves the bloc in March 2019. Without it, Britain could face a legal black hole the day after Brexit.