The EU's chief Brexit negotiator has urged the United Kingdom to begin talks "very quickly".
The Conservative leader lost her parliamentary majority in last week's election and is now desperately seeking the backing of the 10 MPs from Northern Ireland's ultra-conservative Democratic Unionist Party (DUP).
"The talks are ongoing, they are very positive, they are constructive".
Jeremy Corbyn, leader of the opposition Labour Party, which saw its number of parliamentary seats and share of the vote increase, said there could be another election this year or early in 2018 after Thursday's vote produced no clear victor.
"We never put timescales on when we expect a deal to be done and I'm not going to start now".
However, the prospect of a deal has prompted warnings that it could upset Northern Ireland's fragile peace.
She declined to speculate about any change in Britain's plans to withdraw from the European Union following the election, saying, "The citizens have decided, and I assume that we will have to carry out these negotiations".
She told a meeting of backbenchers that she had got the party into "this mess" by calling the snap election and now "I'll get us out of it".
"But we have to be honest, it will take much more than that for us to be convinced that the DUP tail is not wagging the Tory dog", he told reporters.
While the DUP continue to hammer out the details of the arrangement with the Tories, the other four main parties at Stormont confirmed they would be meeting Mrs May on Thursday.
The leader of Britain's House of Commons says the state opening of Parliament will take place on June 21.
Downing Street has insisted that Thursday's general election - which Theresa May had hoped would strengthen her mandate for negotiations but ended up creating a hung Parliament - will not change the approach to Brexit it set out past year.
The Conservative source said: "We're confident of getting an agreement, we're confident that the Queen's speech will be passed".
Before the Mansion House dinner was cancelled because of the fire, finance minister Hammond had been due to tackle fears among the financial elite that May's insistence that "no deal is better than a bad deal" would cost them business.
"She said she will serve us as long as we want her".
Barnier this week acknowledged "sensitivity" in London at European Union suggestions that Britain might owe it some 60 billion euros in 2019 and said sorting out the issue soon would help a trade deal: "I would like to very quickly play down this question, and find concrete, pragmatic and just solutions", he said on Monday.
"Look at what the Tories (Conservatives) have managed to do to the United Kingdom in the space of just one year, firstly calling a divisive and reckless European Union referendum. then having lost that gamble pursuing a hard Brexit path", Scotland's first minister, Nicola Sturgeon, said.
Although there are likely to be some tensions between the Conservatives and the DUP, the two parties have now agreed broad consensus that will give May just enough room to run a government, although nothing like the way she wanted when she called the snap election.