She is also trying to contain outrage at home over a London tower block fire which left at least 30 people dead.
Chancellor Philip Hammond said Britain should prioritise jobs and prosperity and take a "pragmatic" approach as it begins Brexit talks next week.
Following more than an hour of talks between May and DUP leader Arlene Foster on Tuesday, May said the discussion had been productive and Foster said she hoped a deal could be done "sooner rather than later".
Theresa May is now trying to agree a deal with the DUP, after the Tories' majority was demolished in last week's General Election, resulting in a hung parliament.
"There is a unity of goal among people in the United Kingdom", May said following a meeting with French President Emmanuel Macron in Paris.
"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 at Westminster with one of the Northern Ireland parties", he told BBC radio.
But pressure was mounting for May to change course on the type of Brexit Britain should pursue.
Britain will be the first member state ever to leave the bloc.
The report cited unnamed sources, and the finance ministry declined to comment.
Congressman, others wounded in shooting in Va.
He said this reinforces the need for security at any gathering of members of Congress or any lawmaker's public town hall. Staffer Zack BarthZack Barth, a legislative correspondent for Austin Congressman Roger Williams, was shot in the calf.
Hundreds of protesters chanting "we want justice" stormed a local town hall on Friday afternoon and May had to leave a meeting with residents under heavy police guard. Once done, however, Brexit would be hard to reverse.
Having lost a majority in parliament, May needs the DUP's 10 lawmakers to win any kind of vote, including on the pieces of legislation needed to enact Britain's divorce from the EU.
"There is an irony to being lectured about our role in terms of the national government of the United Kingdom when Sinn Féin wants to be in government here in the Republic of Ireland".
Former Conservative prime minister John Major has also raised doubts about the deal and its impact on the province's "fragile" peace.
An election in March saw the Protestant, pro-British DUP finish narrowly ahead of Catholic socialists Sinn Fein.
Northern Ireland's frontier with the Republic of Ireland will be the UK's only land border with the European Union after Brexit.
"We know each other and we understand each other", she said.
The EU's negotiator Michel Barnier dismissed the suggestion of postponing the negotiations and said such a delay would only prompt further instability.
Speaking as he arrived for a meeting of European Union finance ministers in Luxembourg, he said: "As we go into that negotiation, my clear view - and I believe the view of the majority of people in Britain - is that we should prioritise protecting jobs, protecting economic growth and protecting prosperity as we enter those negotiations and take them forward".
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