BERLIN - A collapse of Europe's Schengen passport-free travel zone could cost the European Union up to 1.4 trillion euros over the next decade, a study by Germany's Bertelsmann Foundation showed on Monday.

The study estimated that under a worst case scenario, in which the reintroduction of controls at EU borders pushed import prices up three percent, the costs to the bloc's largest economy Germany could be as much as 235 billion euros between 2016 and 2025, and those to France up to 244 billion.

At a minimum, with import prices rising one percent, the study showed that a breakdown of Schengen would cost the EU roughly 470b euros over the next decade.

The cost would climb to 1.4 trillion euros, or roughly 10 percent of annual GDP in the 28-member EU bloc, under the more dire scenario. "If border controls are reinstated within Europe, already weak growth will come under additional pressure," said Aart De Geus, president of Bertelsmann.

Schengen was established over 30 years ago and now counts 26 members, 22 of which are EU members. But the system of passport-free travel has come under severe pressure over the past half year due to a flood of migrants entering Europe, mainly from the Middle East and Africa.

To stem the tide and to ensure they have an overview of who is entering their territory, many countries within Schengen have reintroduced border controls in recent months, leading to fears the whole system could collapse.

Underscoring the urgency of the issue, Germany's Interior Minister Thomas de Maiziere told public broadcaster ARD on Sunday that EU member states, which have been squabbling for months over how to tackle the migrant crisis, must agree a common approach within two weeks if they wanted to avoid such a fate.

In addition to being a devastating symbolic setback for Europe, a collapse of Schengen would increase the amount of time it takes for goods to be transported across European borders, raising costs for companies and consumers.

The Bertelsmann study, conducted by Prognos AG, estimated that the minimum costs to Germany and France would be 77 billion euros and 80.5 billion euros, respectively, over the period to 2025.

A collapse of Schengen would also increase costs for countries outside the zone, with the combined burden on the United States and China over the next decade estimated at between 91 billion and 280 billion euros, according to the study.