The EU has insisted that it will only talk about a future relationship with the United Kingdom once sufficient progress has been made on divorce terms.
But Mr Davis insisted the United Kingdom still wants to negotiate its future trade relationship with the European Union "alongside" talks on the terms for Brexit, which he said was the process set out in Article 50 of the European Union treaties.
Prime Minister Theresa May in March formally notified the European Union of its intention to leave, starting a two-year timetable for negotiating the exit.
Negotiations had been expected to begin next week but May's loss of her parliamentary majority in a general election last week raised doubts about the date. The queen's speech, which lays out the government's program, has been delayed until Wednesday.
An EU official close to the matter said the "softer Brexit" talk could be "productive" and help progress in the first months, where the British attitude to discussing the financial settlement "will be the first serious test of the negotiations".More news: Rangers log four HRs to beat Mariners, 10-4
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"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", the statement said.
"It is indeed our understanding that the agenda of the first negotiation round consists of issues related to the first phase of negotiations, which means citizens, money, Northern Ireland and some other exit-related questions", one diplomat said. "But the withdrawal and future are intimately linked".
"I'm not going to give a blow by blow account of how we propose to take that discussion forward", he said. Divorce talks are set to begin next week as the anniversary of the Brexit vote nears.
In contrast to May's uncompromising tone with its focus on controlling immigration, Hammond has long stressed the importance of ensuring that British employers can continue to find the skilled workers they need from the EU. The afternoon session consists of working groups and other meetings before a press conference at around 6:30 p.m.