The landmark negotiations will begin on Monday when Brexit secretary David Davis meets European Union representative Michel Barnier in Brussels, nearly exactly a year after the United Kingdom first voted to leave the EU.
Mrs May's weakened position in the House of Commons as a result of losing her majority has fuelled speculation the Tories would be forced to soften their stance on Brexit.
Brexit talks will begin Monday.
"She is fine, she is getting on the with the job", Davis said when asked how May was.
"We've set out the broad principles from where we will start the negotiation and we will negotiate in good faith, but it is a negotiation and we recognize there will be an exchange of views and we will take that forward in a spirit of genuine cooperation", Chancellor of the Exchequer Philip Hammond told reporters in Luxembourg on Friday.
May says Brexit talks to start as scheduled
Tory chief whip Gavin Williamson, who flew to Belfast for talks with the DUP at the weekend, took the lead for the Conservatives . Ireland's Prime Minister Enda Kenny has warned May that deal might endanger peace.
Hammond, speaking to reporters before a meeting of the 28 European Union finance ministers on Friday, said Britain should work closely with the bloc to prioritise jobs and prosperity when Brexit talks start next week.
A joint statement said: "Michel Barnier, the European Commission's Chief Negotiator and David Davis, Secretary of State for Exiting the European Union, agreed today to launch Article 50 negotiations on Monday June 19".
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. The talks are taking place three months after Prime Minister Theresa May formally triggered the two-year Brexit timetable.
His comments Friday come a day after Hammond cancelled a keynote address to London financiers in the wake of the Grenfell Tower disaster. "We believe that the withdrawal process can not be concluded without the future relationship also being taken into account".
Since last week's general election, there have been calls for a new cross-party approach to talks, but Downing Street has said its strategy will not change.
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