"[But] there is no change in content", he said. Many of them suspect the British leader is pursuing a strategy of delay created to push negotiations to the brink, at which point Europe would yield and the hardcore Brexiteers in the British Parliament would be hard-pressed not to accept May's version of withdrawal, even if they despise it as a capitulation.
The summit also was meant to lay the groundwork for an additional planning meeting next month for the U.K.'s exit - though, as the BBC writes, it's possible that European Union leaders will formally say they are going to use the November gathering to prepare for that no-deal scenario.
The two sides are now proposing an implementation period from 30 March 2019 until 31 December 2020.
An offer of an extension clause on the 21-month transition period had already been made by the European Union during the recent secretive round of talks, as first revealed by the Guardian. The EU says a time limit would defeat the point of the backstop.
Number 10 did say progress had been made on the vital issues of the future trade framework, and the notion of a whole United Kingdom backstop for both customs and some single market regulations.
Mr Tusk has warned that without new "concrete proposals" from the British to break the logjam over the Irish border backstop, further progress on a deal may be impossible.
"The Prime Minister and her Government are too weak and too divided to protect people's jobs, our economy or ensure there is no hard border in Northern Ireland", he said.
The British Prime Minister was due to address leaders of the 27 remaining EU states before they discuss Brexit in her absence at the European Council on Wednesday evening.
May was also meeting European Council President Donald Tusk, who a day earlier implored May to present new ideas at the summit for resolving the sticky problem of how to keep the border between the Republic of Ireland and the UK's Northern Ireland friction-free once Britain no longer is an EU member. Brexit must be orderly for everyone and for all the issues including the island of Ireland.
The UK has said the transition period, dependent on an overall deal being agreed, is necessary to stop a "cliff-edge" for business and give the two sides time to agree their future relationship. "We continue to do the work in the next weeks calmly and patiently".
It was hoped that today's meeting would be a prelude to discussing a deal ready for finalisation in November.
"Today there will be no breakthrough", said Lithuanian President Dalia Grybauskaite.
The chancellor said, "It is only fitting as a responsible and forward-thinking government leadership that we prepare for every scenario - that includes the possibility of Great Britain leaving the European Union without an agreement".
Mrs May replied: "We've been very clear throughout the negotiations in relation to the financial settlement that led to the figure of around £39 billion following the December joint report, that this is a country that honours its legal obligations and we will do exactly that". And now, just days before the deadline, they are still bickering amongst themselves.
The cabinet meeting yesterday did not consider a specific wording on any deal, nor make any decisions, but was a discussion about the negotiations and unity.