In calling the election back in April, the Prime Minister asked the electorate to give her a mandate for a hard Brexit, based on Britain leaving the European single market and making a clean break with the EU.
Mr Hammond said: "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, protecting prosperity as we enter those negotiations and take them forward".
Britain gave official notification that it would leave the European Union at the end of March, meaning it will leave the bloc, which is its biggest trading partner, in March 2019.
Following the election outcome, May is forced to seek cross-party political consensus over the UK's exit from the European Union.
"There is a unity of goal among people in the United Kingdom", May said following a meeting with French President Emmanuel Macron in Paris.
"If the Government cannot even secure a deal with the DUP, how on earth can they get a deal with the EU?"
EU planning grand ceremony to honour visionary Kohl
Jean-Claude Juncker told Sunday's Bild am Sonntag newspaper that he will personally push for a "European act of state" for Kohl, who was chancellor from 1982 to 1998, but didn't give details.
The newly-appointed Environment Secretary said the European Union referendum result must be honoured but it is "really important" that the exit package is "in the interests of the whole country".
Pro-Brexit Tory minister Michael Gove meanwhile said Britain would leave the group in line with government policy before the election.
Meanwhile, DUP leader Arlene Foster has returned to Northern Ireland, leaving DUP colleagues to continue talks with the Conservative Party.
Earlier, German Finance Minister Wolfgang Schaeuble made very similar comments on the possibility of Britain staying in the EU.
The Democratic Unionist Party wants to attach its own conditions onto Brexit as part of its deal with the Conservatives - including the insistence on a "soft border" between Northern Ireland and the Irish Republic.
The performance of the British economy could also influence perceptions: Data on Wednesday showed average weekly pay in the three months to April was down 0.4 percent, year-on-year, in inflation-adjusted terms - the biggest fall since the three months to September 2014.