"EP text will now reflect this & insist agreement translated into legal text ASAP", Mr Verhofstadt tweeted.
One said Mr Davis' comments were a "risk to undermine the good faith that has been built during the negotiatioins".
He added: "After David Davis' unacceptable remarks it's time the United Kingdom government restores trust".
The European Parliament is set to back in a vote today the opening of the second phase of Brexit talks.
Irish concerns to copperfasten in a "withdrawal treaty" commitments made on avoiding a hard Border with the other first-phase deal priorities are also being actively addressed, sources say.
In contrast to Mr Davis, Irish prime minister Leo Varadkar has however publicly state that the deal is in fact "bulletproof".
Britain's Brexit minister David Davis caused alarm by saying that a crucial agreement struck last Friday on separation arrangements was a "statement of intent" rather than "legally enforceable".
European Commission spokesman Margaritis Schinas said that while the deal was not legally binding, it was regarded as a pact of honour.
The European Parliament's Brexit pointman Guy Verhofstadt said Davis's comments at the weekend were "unacceptable" and would lead to a "hardening of the position" of the EU.
Gabriele Zimmer, leader of the left group, Philippe Lamberts and Ska Keller, leaders of the Green group, and Danuta Maria Hubner, chair of the Parliament's constitutional affairs committee, have also put their names to it.
A diplomatic draft of the summit...
'This, as far as we're concerned, is a binding agreement - an agreement in principle'.
She told MPs: "It is clear in the joint progress report that this offer is on the table in the context of us agreeing the partnership for the future, agreeing the next stage, and agreeing the partnership for the future", she said.
Although the precise shape of the UK's "no hard Border" commitment will not emerge until its trade relationship with the European Union is agreed in talks that can not start until after Brexit, well after the withdrawal agreement will be signed, Irish officials and lawyers are understood to be working with the commission on means of expressing those commitments in the treaty.
But he later told LBC: "What I actually said yesterday, in terms, was we want to protect the peace process, we want to protect Ireland from the impact of Brexit for them". That just sounds weird to me.