By Gabriela Baczynska and Tom Körkemeier

AMSTERDAM (Reuters) - European Union interior ministers urged Greece on Monday to do more to control the influx of migrants, some threatening to have it excluded from the continent's prized passport-free travel zone as the crisis increasingly divides bloc members.

Greece was the main gateway to Europe for more than a million refugees and migrants who reached the EU last year. It has been criticized for a failure to control the flow of arrivals, which has shown little sign of easing over the winter.

Some member states said Athens must deliver on obligations to alleviate the crisis, which has put the passport-free Schengen zone - hailed by many as the greatest achievement of European integration - on the verge of collapse.

"If we cannot protect the external EU border, the Greek-Turkish border, then the Schengen external border will move toward central Europe," said Austria's Interior Minister Interior Minister Johanna Mikl-Leitner.

"Greece must increase its resources as soon as possible and accept help," she 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.

Overwhelmed by the influx, Greek law enforcement officials have often let migrants through deeper into Europe rather than keep them on Greek soil for proper registration - the first necessary step agreed by the EU before people can move further.

Athens says the numbers are impossible to manage and accuses the other 27 EU states of not offering the right help and not taking migrants from Greece they had committed to move.

Greek migration minister Yannis Mouzalas denounced the threat of Schengen exclusion as "blame game". Athens' public order minister Nikos Toskas said sometimes only several miles separated the Greek and the Turkish border meandering between small islands in the Aegean sea where the refugees travel on small, easily capsizeable boats.

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"It is very difficult to stop small boats coming... except sinking or shooting them, which is against our European values and Greek values and we will not do that," he said.

TEMPORARY CONTROLS

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."

Excluding Greece would require applying Article 26 of the Schengen code that allows temporary border controls within Schengen for up to two years.

Germany, main destination for refugees and migrants fleeing war and poverty in the Middle East and Africa, hopes a November deal agreed with Turkey will mean fewer migrants arrive in Greece. But it is yet to bear fruit.

Greek officials said other EU countries had been too slow in providing everything from funds and border guards, to finger-printing equipment, ambulances and beds.

They criticized the states that reintroduced border controls inside Schengen.

"It's one thing to understand that a country is in panic, is afraid and closing borders. And it's another issue to accept that the European crisis will be a humanitarian crisis in Greece with thousands of trapped refugees and migrants," Mouzalas said.

(Additional reporting by Alastair Macdonald, Writing by Gabriela Baczynska; Editing by Ralph Boulton)