Davis was received by Sweden's EU-minister and they both held a joint press conference on Tuesday morning. The mood was very amicable, with both Davis and Linde stressing how much the two countries have in common.
We voted together more than any other two countries, I think," Davis said about Sweden and the UK in the EU.
Ann Linde made clear that Sweden will remain part of the EU and is not prepared to do any separate deals with the UK.
"We will be represented by a negotiation team led by Michel Barnier from the EU commission, and you will see us unite behind Barnier," she said, adding that the two ministers had not had a "negotiation" today, but a "good discussion" on the positions of the London and Stockholm governments.
And David Davis stressed that the UK wants an outcome of the negotiations that benefits both the UK and the EU.
We are not going away. We're going to leave the EU, but we are still going to be good Europeans," he said.
On the topic of the 100,000 Swedes currently in the UK, and the 32,000 Britons residing in Sweden, Davis got several questions from the journalists as to what will happen to them, how they should be thinking in terms of residency permit, pensions and so on.
We are determined that they will have a good, stable arrangement in the future which protects all aspects of their position, and we intend the same for British citizens abroad too. And we aim to get that resolution as fast as we possibly can," said Davis.
"Had it been possible, we would have done it in December. It will be the very first thing on the agenda. Of course it is a negotiation. But I don't see any reason for anybody to hold this up, once the negotiations start properly," he said.
Davis reconfirmed the timetable, saying that Britain would evoke article 50 before the end of March.