AMSTERDAM (Reuters) – The European Union edged closer on Monday to accepting that its Schengen open-borders area may be suspended for up to two years if it fails in the next few weeks to curb the influx of migrants from the Middle East and Africa.

After chairing a meeting of EU counterparts in Amsterdam, the Dutch migration minister said they expected an unprecedented prolongation of the time governments can impose border checks because the migrant crisis would not be under control before current, short-term dispensations expire in May.

Some ministers made clear such a — theoretically temporary — move would cut off Greece, where more than 40,000 people have already arrived by sea from Turkey this year despite a deal with Ankara two months ago to hold back an exodus of Syrian refugees. More than 60 have drowned on the crossing since Jan. 1 alone.

Greek officials noted that closing routes northward, even if physically possible, would not solve the problem. But electoral pressure on governments, including in the EU’s leading power Germany, to stem the flow and resist efforts to spread asylum seekers across the bloc are making free travel rules untenable.

“We are running out of time,” said EU Migration Commissioner Dimitris Avramopoulos as he urged states to implement agreed measures for reducing and controlling movements of migrants across the continent — or else face the collapse of the 30-year-old Schengen zone, a major EU achievement.

But Dutch minister Klaas Dijkhoff said time has effectively already run out to preserve all of the passport-free regime that has allowed hundreds of thousands of people to trek from Greece and Italy to Germany and Sweden over the past year.

“The ‘or else’ is already happening,” he said. “A year ago, we all warned that if we don’t come up with a solution, then Schengen will be under pressure. It already is.”

The piecemeal reintroduction of controls by several governments under pressure from domestic opinion at national borders with fellow EU states should be better coordinated, said Dijkhoff, whose government last year floated the idea of a “mini-Schengen” that critics saw as a way for Germany and its northern neighbors to bar the influx from the Mediterranean.

German Chancellor Angela Merkel, who opened her country’s borders to Syrians fleeing civil war last summer, is under mounting pressure to halt the inflow after more than a million migrants entered Germany last year.

Without a clear drop in the numbers arriving before she meets fellow EU leaders at a summit in mid-February, some form of border closer by the bloc’s leading power, which would have a knock-on effect across Europe, would be increasingly likely — not least as Germans vote in key regional elections in March.

The Commission, the EU executive, is already conducting a review of whether Greece’s difficulty in processing constitute “persistent serious deficiencies” on the external EU frontier that would justify a historic move to allow states to reimpose controls on those arriving from Greece.

It is due to make recommendations next month and Athens would have three months to respond. Existing measures taken by some states under a different rule expire in mid-May. Minister Dijkhoff made clear that few expect the situation to be under control by then, so the longer-term suspension should be ready.

Under that measure, Article 26 of the Schengen code, states could reimpose controls on documents for six months, renewable three times, until May 2018. EU officials acknowledged, however, that no one knows what would happen after that if governments were not prepared to return to the status quo before last year.

“Everyone understands that the Schengen zone is on the brink,” Austrian Interior Minister Johanna Mikl-Leitner said.

“If we cannot protect the external EU border, the Greek-Turkish border, then the Schengen external border will move towards central Europe … Greece must increase its resources as soon as possible and accept help.”

The Schengen zone comprises 26 states, most of which are also EU members. Germany, France, Austria and Sweden are among several countries that have introduced temporary border checks as they struggle to control the flow of people.

“Speaking about timetables, it’s already too late. We have seven countries with border controls,” Sweden’s interior minister Anders Ygeman told Reuters.

He said migrant registration centers need to start functioning in Greece and Italy as planned: “In the end, if a country doesn’t live up to its obligations, we will have to restrict its connections to the Schengen area.”

Appearing anxious to calm a confrontation with the radical leftist government in Athens that already clashed with Berlin last year over its demands of bailout loans to keep Greece in the euro zone, his German counterpart was more reserved.

“Blaming people in public doesn’t help,” Thomas de Maiziere said.

The EU has taken various steps to give cash-strapped Athens financial assistance to deal with the crisis, but many member states believe Athens is not using that enough. Of five registration “hotspot” centers due to be set up for migrants arriving in Greece, only one is running so far.

(Writing by Alastair Macdonald; Editing by Richard Balmforth)