Theresa May called for Brexit talks to "accelerate and intensify" after she left a stormy European Union summit dominated by the migration crisis.

The Prime Minister used the summit to issue a stark warning to EU leaders about the risk to their citizens' safety if a Brexit deal on security was not reached and indicated the negotiations on the UK's exit were about to enter a new phase with the publication of the Government's long-awaited White Paper.

But her address to EU leaders in Brussels was a sideshow in a marathon session of talks on the migration crisis which began on Thursday evening over dinner and stretched into the early hours of Friday.

Confirmation that a compromise had been reached only came shortly after 4.30am local time when European Council president Donald Tusk tweeted that conclusions had been agreed.

For Mrs May, the drawn-out summit was an opportunity to update EU counterparts on the latest developments in the Brexit process and a chance to spell out what was at stake if a deal on security information-sharing is not reached.

The other 27 EU leaders will continue their meeting on Friday in Mrs May's absence as they discuss their approach to the future relationship between the UK and Brussels.

At the gathering it was clear they were becoming impatient at the Prime Minister's inability to provide a clear indication of what her divided Cabinet wants to achieve.

As she left the Brussels summit, Mrs May said: "We are going to be publishing our White Paper shortly and I want to see the negotiations accelerating and intensifying thereafter."

She urged EU leaders to change the mandate given to their negotiators in order to allow UK involvement in key law enforcement initiatives including the Prum mechanism for sharing DNA profiles and other data, the Second Generation Schengen Information System (SIS II) database of "real-time" alerts about individuals interest to EU law enforcement and the European Criminal Records Information System (ECRIS).

Without a deal "we would no longer be able to share real-time alerts for wanted persons, including serious criminals" and "our collective ability to map terrorist networks across Europe and bring those responsible to justice would be reduced", she told her counterparts.

A senior UK source said: "European negotiators have put obstacles in the way of reaching agreement on mapping the movement of terrorists and criminals and sharing vital information."

Mrs May's intervention on Brexit over dinner was only the starter to a full-blown row on the migration crisis.

The issue has assumed greater political significance in Europe because of the threat to German chancellor Angela Merkel's position over her approach to letting migrants settle in her country.

Meanwhile Italy's Giuseppe Conte used the summit to demand a fundamental change in the bloc's migration policy, saying that his country received little help even though it was at the forefront of receiving migrants from across the Mediterranean.

Speaking shortly after 5am in Brussels, Mrs May acknowledged there had been "lengthy discussions" on the EU's approach.

"We have come to positive conclusions, a lot of them around what the United Kingdom has been encouraging for some time, which is taking more action upstream in countries of origin so that we can ensure that people aren't having to make and aren't making these very dangerous journeys, often travelling many miles, often at the hands of the people smugglers and making the dangerous trips across the Mediterranean where we still see some people dying."

EU diplomats said that the leaders finally found agreement on a vaguely worded concept centring on reception centres to deal with migrants and asylum seekers in EU nations which would volunteer to have them.

Mr Tusk had pushed the idea of "regional disembarkation platforms" - facilities outside the EU where would-be travellers to Europe are processed to decide whether they are refugees or economic migrants.