The pair will meet again before the end of the month, with time running out before the UK leaves the EU on 29 March, and ahead of what could be the decisive vote in the House of Commons next week.
In a joint statement, Mrs May and Mr Juncker said future talks should be held in a “positive spirit” and committed to looking at “guarantees” that could be given on the “temporary nature” of the controversial Irish border backstop.
However, the statement reaffirmed a letter sent by Mr Juncker and EU Council President Donald Tusk on 14 January, which states that Brussels is “not in a position to agree to anything that changes or is inconsistent with the Withdrawal Agreement” already agreed with the UK.
It again puts the Prime Minister on a collision course with Brexiteers in her own party next week, unless a breakthrough can be made before the weekend, when Mrs May joins EU leaders at a joint summit with the Arab League in the Egyptian resort of Sharm el-Sheikh - the last chance for the other 27 member states to sign off a compromise before votes in the Commons.
However, British officials stressed they were not expecting any decisions relating to the Brexit negotiations in Egypt. “This is not a meeting about Brexit and the Prime Minister is not going to seek to turn it into one,” one official said.
Before their meeting, Mr Juncker had downplayed UK government briefings that a breakthrough was near. “Each time that the prime minister expresses her wish to come we will always be happy to listen to her and see what she has to say,” the Commission chief said.
He appeared at their photocall with a bandage on his face from a shaving cut, joking that Mrs May had not given him the injury.
Speaking in Berlin as part of an intense Brexit diplomatic offensive, Foreign Secretary Jeremy Hunt said the key to getting a deal approved by MPs was securing changes which would allow Attorney General Geoffrey Cox to alter his legal advice that the UK could potentially be trapped in the backstop indefinitely. Mr Cox is expected to address MPs today.
“If we solve the issue of the backstop then we can pass this deal through parliament,” Mr Hunt said.
The Foreign Secretary warned European leaders that the continent would be deeply damaged if a deal was not reached.
“We do not want historians to puzzle over our actions and ask themselves how it was that Europe failed to achieve an amicable change in its relationship with Britain – a friend and ally in every possible sense – and thereby inflicted grave and avoidable damage to our continent,” he said.
Mr Hunt also played down the prospect of an extension to Article 50, despite warnings of ministerial resignations without a Brexit delay.
“The last thing that people in the UK and indeed the rest of the EU want is Brexit paralysis,” he said.