The Prime Minister has insisted the United Kingdom will leave the single market, replace customs union membership with a new deal and end the jurisdiction of the European Court of Justice.
In a hint at a softer approach, Mr Davis said on Monday "we will start down this process" by focusing on the divorce proceedings from the European Union before moving on to trade.
"It's a unity of objective, having voted to leave the European Union, that their government gets on with that and makes a success of it". "We want to end the anxiety facing 4 million citizens".
May left Downing Street without responding to reporters' questions on whether an agreement had been reached with the DUP, which is needed to help the Conservatives command the majority they lost in last week's election.
Any deal Northern Ireland's Democratic Unionist Party reaches to prop up British Prime Minister Theresa May must not interfere with devolution in the British province, Ireland's new prime minister said on Friday.
While the DUP are deeply eurosceptic, they have balked at some of the practical implications of a so-called hard Brexit - including a potential loss of an open border with the Republic of Ireland - and talks will touch on efforts to minimise the potential damage to Northern Ireland.
Her spokesman said Britain would not change its stance on Brexit, though May told her lawmakers she would seek a broader consensus in the party on her approach.
The Conservatives are yet to agree a deal with the DUP, a week after the general election stripped May of her parliamentary majority.
Earlier, Andrea Leadsom, leader of the House of Commons, said the government had agreed with Queen Elizabeth, who reads out the new government programme, that the "state opening of parliament will take place on June 21, 2017". "I got us into this mess, and I'm going to get us out", she said. Data on Wednesday showed average weekly pay in the three months to April fell by 0.4 per cent on the year in inflation-adjusted terms - the biggest fall since the three months to September 2014.
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".