Theresa May has reassured leaders that Brexit will not mean paring back relations with EU countries.
The prime minister was holding talks with leaders like Germany's Angela Merkel, Spain's Mariano Rajoy, and Austria's Christian Kern at a one-day European summit in Malta.
Following their conversation, in which she updated Mr Rajoy and Mr Kern on the UK's preparations for Brexit, Mr Rajoy said her speech "clarified many things".
A Downing Street source said: "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."
They also agreed that an early deal on the rights of EU citizens in the UK, and British citizens in the EU, was desirable.
More than 700 people have been rescued from the Mediterranean in the last 36 hours.
The UK will offer help to Latin American and Asian countries which need migrants, to be able to take them in.
The European Union summit will see leaders discuss the migrant crisis between Italy and Libya, defence and Nato, and Donald Trump.