She met DUP leader Arlene Foster, whose Eurosceptic Northern Irish party has 10 parliamentary seats, for more than one hour of talks in Downing Street.
As Britain entered a sixth day of political turmoil, Mrs May's team continued talks with Northern Ireland's Democratic Unionist Party (DUP) to secure their support after the Prime Minister failed to win a majority in last Thursday's election.
Opposition Labour leader Jeremy Corbyn congratulated May on "returning as PM" and said he "looked forward to this parliament, however short it may be", in reference to her weakened support base as the head of a minority government. "I hope that we can reach a conclusion sooner than later", Foster said.
Ms May faces the task of satisfying both the pro-European and eurosceptic factions of her party, keeping Northern Ireland calm and negotiating a divorce with 27 other European Union members whose combined economic might is more than five times that of Britain.
Former Prime Minister John Major said he was concerned a deal with the DUP could thrust the province back towards violence almost two decades since a US-brokered peace deal brought peace to Northern Ireland.
And despite French President Emmanuel Macron stating the United Kingdom could still opt to remain an European Union member, Verhofstadt added this would not mean a return to previous circumstances.
"They would see it as the government paying cash for votes in parliament, and in doing so I think that could well cost votes in the country for the Conservative party, by the bucketload, at a subsequent election", he said. "I can't negotiate with myself", Mr Barnier was quoted as saying by the Financial Times.
Under the confidence and supply arrangement being mooted by the Tories and the DUP, the Northern Irish party's 10 MPs would lend its support to the Government for key votes - such as passing the Budget and the Queen's Speech.
The Prime Minister will meet separately with representatives of Sinn Fein, the Ulster Unionists, the SDLP and the Alliance Party - as well as the DUP - in Downing Street in an attempt to allay growing concerns.
"Westminster has brought us austerity, has brought us hardship, and it has hurt the working class people in our communities", one of their MPs told reporters at a news conference in London.
"That is why we're ready to start very quickly".
May faced her lawmakers at a meeting of the 1922 Committee on Monday.
So far issues between the two parties have stopped an agreement.
David Davis is in charge of heading up negotiations as Britain leaves the EU How would it be different to a hard Brexit?
The talks are being closely watched in European capitals as they could delay the expected start of Brexit negotiations next week, as well as change Britain's entire approach to its EU withdrawal.
"The danger is that however much any government tries they will not be seen to be impartial if they are locked into a parliamentary deal", former Conservative prime minister John Major told BBC radio.