The European Parliament is to demand that last week's Brexit deal is converted into a legally binding text as soon as possible.
The parliament's chief Brexit co-ordinator Guy Verhofstadt said suggestions from David Davis that the agreement was not binding had undermined trust in the UK among MEPs.
In a TV interview on Sunday, Mr Davis appeared to suggest that the UK could seek to alter agreements on divorce issues including the Irish border, citizens' rights and the UK's £39 billion financial settlement, saying the deal was "much more a statement of intent than it was a legally enforceable thing".
After the Irish Government branded the comment "bizarre", the Brexit Secretary took to the airwaves once again on Monday, saying that Britain's commitment on the border issue was "much more than just legally enforceable".
The European Commission spokesman Margaritis Schinas later confirmed that the joint report published last week by Mr Davis and EU Brexit negotiator Michel Barnier was "not legally binding" until it is incorporated in a formal Article 50 Withdrawal Agreement, expected in the autumn of 2018.
But asked if it was therefore possible for either side to back down on it, Mr Schinas stressed that it was regarded in Brussels as "a deal between gentlemen" which was "fully backed and endorsed" by the UK Government. He noted that Prime Minister Theresa May and Commission president Jean-Claude Juncker had shaken hands on it.
Mr Verhofstadt suggested that MEPs would like to bring forward moves to make the agreement legally binding.
"Remarks by David Davis that Phase One deal last week not binding were unhelpful and undermine trust," he said in a tweet.
"European Parliament text will now reflect this and insist agreement translated into legal text ASAP."
Mr Verhofstadt said the UK must "stick to its commitments" and put them into a draft Withdrawal Agreement "as soon as possible" if there is to be progress in the second phase of negotiations, on trade.
He has tabled two amendments for MEPs to consider in the European Parliament, one of which says Mr Davis's comments "risk to undermine the good faith that has been built during the negotiations".
Another calls on Britain to "fully respect" last week's Brexit deal and ensure it is "fully translated" into a draft Withdrawal Agreement.
Mr Verhofstadt said he introduced the amendments alongside four other European Parliament groups, including the PPE group led by Manfred Weber, a close ally of German Chancellor Angela Merkel, as they are concerned about the "unacceptable description by David Davis of this agreement, saying it was merely a statement of intent, rather than a legally enforceable text".
Responding, Mrs May's official spokesman told a regular Westminster briefing: "The Secretary of State set out yesterday - and the commission agreed with him - that the agreement that was reached last week is a political agreement but that will move forward into a Withdrawal Agreement which will be legally binding.
"The commitment is clear from the Prime Minister and the Secretary of State for Exiting the European Union that we don't want a hard border. I think everybody understands that."