European leaders are watching the relationship between Theresa May and Donald Trump with suspicion, according to ITV News Europe Editor James Mates.
At the first EU summit since President Trump was sworn in, French President Francois Hollande said Donald Trump was putting "unacceptable pressure" on the union.
European Commission president Jean-Claude Juncker echoed Mr Hollande's criticism, suggesting Mr Trump "does not know Europe".
Although leaders believe that she did good work on convincing Trump to continue supporting Nato, she also pressed her counterparts to commit to spending 2% of GDP on defence, as per Nato rules.
There are suggestions that, if the Trump administration continues being antagonistic, EU leaders think the UK will need to choose whether to enjoy a close relationship with Washington, or with Brussels.
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.