David Davis is taking his Brexit message across Europe after suffering a setback in Brussels.
The Brexit Secretary is meeting members of Spain's government as part of his effort to build bridges across the continent.
Mr Davis's meeting with the administration of prime minister Mariano Rajoy came after a setback in Brussels saw UK officials agree to the Brexit timetable set out by the European Commission's chief negotiator Michel Barnier.
Talks in Spain are expected to include the thorny issue of Gibraltar after the EU's guidelines for talks suggested the disputed territory's future economic status might be subject to a veto from Madrid.
British sources have insisted the sovereignty of the Rock is not up for discussion as part of the Brexit talks, which began in Brussels on Monday.
The Brexit Secretary had wanted trade talks to take place in parallel with negotiations on the divorce from Brussels but the UK reluctantly accepted the timetable set out by Mr Barnier.
Mr Davis said he was optimistic about the process and the British appeared upbeat about the prospects of trade talks beginning before the final details of divorce proceedings had been agreed.
Prime Minister Theresa May spoke to Polish counterpart Beata Szydlo about the negotiations, telling her she wanted a "deep and special partnership that supports a strong and prosperous EU" and stressing her commitment to a deal on the rights of EU citizens.
Mr Barnier warned the UK faced "substantial" consequences as a result of Brexit but insisted it was "not about punishment" or revenge.
In a reference to the Prime Minister's negotiating mantra, he said: "For both the European Union and the United Kingdom, a fair deal is possible and far better than no deal."
After the first day of the negotiations, which could shape the UK's economic and political future for a generation, it was agreed that working groups of officials would aim to make progress on the issues of citizens' rights, the UK's financial settlement, the so-called divorce bill, and other issues to do with separation.
The most senior officials on either side will lead work on efforts to resolve the problem of the border between Northern Ireland and the Republic of Ireland, a situation Mr Barnier acknowledged is politically sensitive at a time when the Tories are seeking the support of the Democratic Unionist Party to prop up Mrs May's minority government.
Only when "sufficient, concrete progress" on the first phase has been made will Mr Barnier recommend to the European Council that the negotiations can enter the next stage, taking in the future trading relationship, with that recommendation possibly coming at October's summit of EU leaders.
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.
Both sides acknowledged the clock was ticking, with the date for the UK's departure from the EU fixed for March 2019.
Mr Davis denied suggestions the agreed timetable showed Britain's "weakness" and insisted it is "completely consistent" with the Government's aim of parallel trade and exit talks.
"It's not when it starts, it's how it finishes that matters," he said.
"The UK has been crystal clear in our approach to the negotiations, the withdrawal process cannot be concluded without the future relationship also being taken into account.
"They should be agreed alongside each other, this is completely consistent with the council's guidelines which state nothing is agreed until everything is agreed."
The Brexit negotiations started as International Trade Secretary Liam Fox met US trade representative Robert Lighthizer in Washington.
The two men discussed the possibility of laying the groundwork for a new potential trade agreement between the UK and US after Brexit.
Dr Fox said: "Our valuable talks underlined the shared interest in forging a closer trade and economic relationship including making progress on policy co-ordination, regulatory issues and expanding trade and investment between our economies.
"As our largest single trading partner, we have a strong foundation to build on as we start preparation on joint work to explore a future ambitious trade agreement once the UK has left the EU."
Mr Lighthizer said: "As the United States' fifth largest export market, the United Kingdom is an invaluable trading partner.
"As UK negotiations with the European Union begin, I look forward to working with Dr Fox and the United States Congress to lay the groundwork for our future trade relationship, including exploring the possibility of a new US-UK trade agreement.
"In the meantime, the United States is committed to continuing discussions for improving trade and investment and co-ordinating on addressing global excess capacity issues."