3 February 2017
The prime minister told EU leaders she wanted to build a "strong partnership" with the EU and pledged the UK would be a "good friend and ally" post-Brexit.
But Mrs May was forced to defend her decision to seek a close relationship with US President Donald Trump.
EU leaders have voiced concern over his perceived hostility towards the union.
Mrs May used a summit of EU Nato leaders in the Maltese capital of Valletta to build alliances ahead of Brexit and to brief her counterparts about her recent visit to the White House to meet Mr Trump.
She pledged a further £30m to help with the EU migrant crisis, with the UK providing medical care, temporary shelter and legal support to 60,000 refugees in Greece, Egypt and across the Balkans, while helping to reunite up to 22,000 people with their families.
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EPA
As well as assisting those who want to return home, the UK is offering to work with countries in Asia and Latin America that are willing to welcome refugees but do not have adequate infrastructure in place at present.
While Mrs May did not have a formal bilateral meeting with Mrs Merkel, the two leaders did have a "lengthy discussion" during a walk through Valletta ahead of a working lunch.
The German chancellor told reporters afterwards: "I am pleased that Theresa May says that she wants a strong Europe.
"It's up to us, as the 27, to determine how strong and how good and how rigorous Europe is and how we solve our problems - and Germany wants to do its part on that."
During talks with Spanish prime minister Mariano Rajoy and Austria's Christian Kern, Mrs May promised that the UK would remain a "reliable partner" after Brexit.
Greater certainty
Mr Rajoy said Mrs May's speech setting out the UK's Brexit plans, including quitting the single market, had "clarified many things" and given a greater degree of certainty.
"They agreed that it was important to think about the future relationship as well as the detailed exit arrangement, so that we can give greater certainty for people and businesses who want to live and work in each other's countries," a Downing Street source said.
They also agreed an early deal on the rights of EU citizens in the UK and Britons in the rest of Europe was desirable.
Mrs May's visit comes two days after MPs voted to allow her to get Brexit negotiations under way.
Malta's prime minister Joseph Muscat said while he wants a "fair deal" for the UK after Brexit, it must be "inferior" to full EU membership.
Mrs May also used the summit to add her weight to President Trump's call for European Nato members to meet the target of spending a minimun of 2% of GDP on defence - a mark the UK is one of the few alliance members to meet.
Nato estimates for 2016 show the US, Greece, Poland and Estonia are the only other countries who will fulfil the requirements.
'No anti-Americanism'
The BBC's deputy political editor John Pienaar says it was a tough ask for many European countries, because it would mean doubling their defence expenditure.
And European leaders have expressed concern about Mr Trump's comments about the EU and the US ban on refugees and visa holders from a number of mainly Muslim countries.
They are also anxious about the man tipped to be Mr Trump's EU ambassador, Ted Malloch, who has suggested the union needed to be "tamed".
As part of efforts to build a bridge between Washington and Europe, Mrs May said the president's commitment to her about being "100% behind Nato" underlines the importance of defence and security co-operation.
But Mr Muscat, whose country holds the rotating European Council presidency, said while there were concerns about some of the decisions that are being taken by the new US administration "there was no sense of anti-Americanism" among the 28 EU members.
"There was a sense that we need to engage with the United States just the same, but that we need to show that we cannot stay silent where there are principles involved," he said.
"As in any good relationship, we will speak very clearly where we think that those principles are being trampled on."
European Commission president Jean-Claude Juncker said while he did not feel threatened by Mr Trump "there is room for explanations because of the impression the new administration does not know the EU in detail - but in Europe details matter".
Mr Kern said: "Today we have pretty mixed feelings, to be honest, because the tangible aspects of Mr Trump's policies are raising some concerns.
"It's not a threat, it could be a catalyst for a strong, more united Europe. It is an alarm call to see if we are on the right track."
http://www.bbc.com/news/uk-politics-38849868
