"As we also said in our Article 50 letter, "agreeing a high-level approach to the issues arising from our withdrawal will of course be an early priority". Two former Conservative prime ministers have also urged May to soften her approach.
The announcement followed speculation that talks may have to be delayed because of the inconclusive outcome of last week's General Election, which has already forced the State Opening of Parliament to be put back from June 19 to 21.
"There is a unity of objective among people in the United Kingdom", May said following a meeting with French President Emmanuel Macron in Paris.
The DUP supports Brexit - but also wants to avoid a hard border with the Republic of Ireland and to maintain as far as possible the current access to European Union markets - both of which would be jeopardised if the United Kingdom leaves without a deal in place, an outcome known as a "hard Brexit".
But with so much at stake for Britain and its $2.5 trillion economy, pressure was mounting on May from within and without her party to heed other voices.
The first round of formal negotiations on Britain's withdrawal from the European Union will begin on June 19, it has been confirmed.
Britain will be the first member state ever to leave the bloc.
The chancellor of the exchequer was asked whether he favoured a softer version of Brexit - such as British membership of the EU single market or of a customs union.
Speaking as he arrived for a meeting of European Union finance ministers in Luxembourg, Hammond 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".
Defence Secretary Sir Michael Fallon said the government's view of Brexit had not changed.
"Like Alice in Wonderland, not all the doors are the same".
May has not yet responded to a proposal from some Conservatives for business groups and lawmakers from all parties to agree a national position on Brexit.
He said he believed there was a majority in the Commons for such an approach.