The European Union must assert control of its external borders if passport-free travel among continental countries is to survive, European Council president Donald Tusk has warned.
Mr Tusk was speaking at a summit of European and African leaders in Malta at which the EU launched a £1.3 billion fund to try to ease the flow of migrants seeking to enter the continent from Africa.
David Cameron - who left the summit early to return to the UK for the visit of Indian prime minister Narendra Modi - indicated he is willing to commit almost half a billion pounds from the UK's aid budget over the next five years to Africa and Turkey to address the issue.
The EU fund will be spent on job creation, food security, public services and conflict prevention in Africa, in order to reduce incentives to leave for Europe, as well as funding migration management programmes.
But Senegal's president Macky Sall told reporters that, while the fund was "a very good beginning", it was "not enough for the whole of Africa".
The summit was called in response to a migration crisis which has seen hundreds of thousands of people cross the Mediterranean from Africa and the Middle East and prompted countries including Germany, Sweden and Slovenia unilaterally to impose new controls at their borders.
Mr Tusk said Europe now faced "a race against time" to save the Schengen arrangement - which the UK and Ireland are not part of - under which people can travel between 22 EU members and four other European states without border checks.
"I have no doubt that without effective control of our external borders, the Schengen rules will not survive," said the European Council president.
Home Secretary Theresa May said the Malta summit had seen "very constructive discussions" between EU and African leaders.
"We want to work with African countries which are the countries of origin for these people to ensure that people don't feel the need to make this journey to Europe," she said.
"In the UK we are putting £200 million extra aid into Africa to help ensure we provide the circumstances there that ensure people don't make this journey."
Mrs May said Britain wanted African countries to co-operate in the return of migrants found to have entered Europe illegally. And she said she wanted action "to smash the criminal gangs making money out of human misery".
Downing Street said Britain was offering £275 million over the next two years as part of an EU package to help Turkey cope with the scale of the refugee crisis it faces as a result of the civil war in neighbouring Syria.
The money comes on top of £200 million pledged over the years to 2020 to help African countries address some of the problems which have driven many migrants out of their home countries.
A Number 10 source said: "We are sat in the western Mediterranean, which was the focus at the start of the crisis, but in recent months the focus has been on the eastern and the route from Turkey to Greece where you see a lot more of the numbers of Syrian refugees as opposed to the route where we are sat today, which is more illegal migration.
"We remain really concerned about that route and the support that we should be providing to countries in the region."
The UK money could be used to fund new refugee camps and provisions for those left homeless by the conflict in Syria and to tackle the "small-scale industry" selling rafts to desperate migrants trying to leave Turkey for Europe..
"The more you contain the problem in and around Syria so that if and when you find a solution on Syria it's easier for people to go home," the Downing Street source said.
The money for Turkey and Africa would come out of the 0.7% of gross national income committed to overseas aid.
The Number 10 source said: "It is us looking at how we focus our spending on humanitarian assistance, but also dealing with an issue that has repercussions for us in Britain. So we are investing our aid money upstream and overseas to better manage the problem arriving at our shores."