Theresa may said Britain wants to remain friends with EU at informal Brexit talks in Malta
The Prime Minister also made it clear that Britain wants to remain friends with the EU after Leaving by agreeing to offer cash and assistance to persuade Asian and Latin American countries to take refugees who have landed in Europe.
But with EU leaders wanting to have a united hard response to Donald Trump, Mrs May has defended her position of seeking close ties with the new US President.
Mrs May used the opportunity of a walking tour of Valletta to talk with some of the key players in the forthcoming Brexit negotiations.
The Prime Minister and her European counterparts visited some of the Maltese capital's historic sites during the excursion.
Mrs May took turns speaking to, Angela Markel, Jean-Claude Juncker and Donald Tusk
Earlier, Mrs May’s hopes for an early deal on the rights of British citizens living in the EU after Brexit were given a boost as Spain's Mariano Rajoy backed the plan.
They discussed the issue of reciprocal rights
The Prime Minister has refused to guarantee the status of EU citizens in the UK unless reciprocal arrangements are made for Britons living on the continent.
Spain's agreement on the issue is significant as the country hosts the largest number of Britons living abroad in the European Union and puts pressure on Mrs Merkel who has obstructed an agreement from being signed.
Blair and Juncker: Together through the years
Wed, January 25, 2017
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Former Prime Minister, Tony Blair and President of the European Commission, Jean-Claude Juncker have always shared a friendly relationship over the years.
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EU Commission President Juncker greets former British PM Blair in Brussels
Number 10 said Spanish prime minister Mr Rajoy backed Mrs May's hopes for an early deal during talks on the margins of an EU summit in Valletta.
"They discussed the issue of reciprocal rights, and agreed it would be good to get agreement on this issue early on in the negotiations," a source said.
She also talked to Austria’s Chancellor Christian Kern about her desire for a "strong partnership with the EU in future".
Mrs May also agreed to a £30 million package to offer assistance to countries in Asia and Latin America to take in refugees from Europe.
The new funding will go towards measures to protect vulnerable migrants from freezing conditions and the threat of people-trafficking and sexual violence, but also to encourage them to return home rather than continue perilous journeys to Europe.
Spanish prime minister Mariano Rajoy backed Mrs May's hopes for an early deal
UK money will help countries like Greece, Egypt and the Balkan states provide for refugees who have reached their territory from trouble zones like Syria, and to integrate incomers into local communities.
During the summit Mrs May also told fellow European leaders that they need to bring their defence spending up to two per cent of GDP and share the burden with the UK and USA after she had persuaded Mr Trump to back Nato 100 per cent.
But signalling a harder line against America, Malta's Prime Minister Joseph Muscat – who holds the six-month rotating presidency of the European Council – said the 28 national leaders had voiced "concern" over some of Mr Trump's decisions and attitudes and agreed that it was time for the EU to "lead at a global level".
Mrs May also told fellow European leaders that they need to bring their defence spending up
He said the EU would not let Mr Trump “trample” on its values.
However, Mrs May defended seeking a positive relationship with the US President.
She said: "I was pleased to be able to visit President Trump so early in his administration and, crucially, when I was there I was able to confirm with him his 100% commitment to Nato – Nato, which has helped keep the security of not just the UK but Europe, and is crucial in keeping that security in the future."