At a press conference in Brussels, Mr Davis said: "We discussed two aspects of it".
The border between Northern Ireland, which is part of the United Kingdom, and the Republic of Ireland (Other OTC: IRLD - news), an European Union member, will become the only land border between the UK and the European Union after Britain exits the bloc in March 2019.
Regarding the future relationship with the EU, Davis said Britain has not changed its position, reiterating that Britain will leave the single market and the customs union, which is "the only way" to allow Britain to develop free trade agreements with non-EU countries.
The talks are set to kick off at 11 a.m. (0900 GMT) in Brussels with a meeting between Davis and the EU's chief Brexit negotiator Michel Barnier.
As Europe grows more confident in its future after the election victory in France of pro-EU President Emmanuel Macron and the growing assurance from German Chancellor Angela Merkel that she will be re-elected in September, analysts say there may be fewer reasons for Europe to compromise.
After seven hours of talks in Brussels, Mr Davis, who had previously promised the "row of the summer" over the timetable for the negotiations, remained upbeat.
The start of the negotiations comes as work continues across the British government to prepare Britain for life outside of the EU.
"So we each have to assume our responsibility and the consequences of our decision and the consequences are substantial". He noted the European Union wants to discuss divorce terms before moving on to the shape of its future relations with Britain.
Fakhar, Amir star as Pakistan rout India
His transformation into a hero was complete as his final tally was six overs, two maidens, 16 runs and three wickets. Pakistan coach Mickey Arthur too was a happy man.
Tory Prime Minister Theresa May had called for "parallel talks" on the UK's future relationship with the European Union - primary making early progress on a trade deal.
Mr Barnier and Mr Davis will meet every four weeks over the coming months, bringing their teams together for a matter of days each time.
"The other is the determination to maintain an, as near as possible, invisible border so we do not undermine the peace process, do not provide any cause for concern in Northern Ireland".
Both English and French will be used as working languages in negotiations and working documents, and the two sides have agreed a set of principles on the openness of their talks.
"Where possible, both parties will seek to agree public statements relating to negotiating rounds", the document stated. He said he views the talks with "informed optimism".
"Leaving gives us the opportunity to forge a bright new future for the United Kingdom - one where we are free to control our borders, pass our own laws and do what independent sovereign countries do", he said.
"This is a technically hard issue but it is one which I am certain is soluble, although it will probably take us until the end of the process when we have already decided what our customs and free trade arrangements are".
"In the meantime, the United States is committed to continuing discussions for improving trade and investment and coordinating on addressing global excess capacity issues".
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