"Of course the door is always open as long as the negotiations on Brexit have not finished", Macron said in a press conference.
With Britain entering a sixth day of political limbo as May is yet to seal a deal to prop up her minority government and faces calls to soften her stance on Brexit, May said the timetable for Brexit negotiations remained on course with talks due to start next week.
But he stressed too that he respected the sovereign decision of the British people to leave the European Union in their referendum a year ago, adding that the start of talks was an important milestone.
UK Prime Minister Theresa May has reassured French President Emmanuel Macron that the Brexit talks scheduled to start on June 19 will not be delayed.
On whether the terms of Brexit would now change, the Prime Minister said only: "I think there is a unity of objective among people in the United Kingdom".
May, who had called for a snap election in the hopes of getting an increased majority that could have strengthened her position before going into the negotiations, is now under pressure to resign over her Conservative Party's failure in that election, which was held last week.
However, in Brussels, it was reported that the British delegation was unable to say on what date it wanted the talks to start when asked to do so by Michael Barnier, the European Commission's chief Brexit negotiator.
Portugal's Santos and Ronaldo criticise St Petersburg pitch
T he Germans played out a 1-1 draw with Chile in their second group outing after a 3-2 win over Australia in their first match . In Portugal's first game against Mexico , their back line was exposed as slow to react on crosses.
The poignant moment served to underline May and Macron's main message, namely that France and Britain will continue to work together despite Brexit.
The measures aim "to ensure the Internet can not be used as a safe space for criminals and terrorists and it can not be used to host the radicalising material that leads to so much harm", May said.
Macron's comments echoed others by German Finance Minister Wolfgang Schaeuble on Tuesday.
Mrs May, on her first overseas visit since losing her Commons majority, claimed her government could still represent a "unity of purpose" on Britain's behalf.
It includes exploring the creation of new laws that would impose penalties on internet companies if they failed to act.
The two leaders agreed on an initiative to pressure tech companies to abide by their social responsibility of tackling online extremism and to create "a new legal liability for tech companies if they fail to remove unacceptable content".
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