Turkey’s military push into Syria has sparked fears in Greece, already struggling with an alarming surge in the number of asylum seekers, of a new wave of migration to Europe.

With camps on Aegean islands at breaking point, Athens has insisted the topic should be discussed at this week’s EU summit. “Europe shouldn’t be caught unprepared again,” Giorgos Koumoutsakos, the Greek minister for migration policy, told local media. “Nobody can be certain what is going to happen.”

Turkey’s president, Recep Tayyip Erdoğan, ratcheted up the rhetoric last week by threatening to “open the gates” for the 3.6 million refugees in his country if Brussels called the military operation in Syria’s Kurdish-occupied north-east an invasion. The Assad regime’s continued bombardment of Idlib, the last rebel stronghold in Syria’s north-west, has added to the concerns of an emerging humanitarian and security crisis on the bloc’s southern flank.

After visiting Athens and Ankara this month, Germany’s interior minister, Horst Seehofer, warned of a repeat of the chaos when close to a million displaced Syrians traversed Greece en route to mainland Europe in 2015.

“If we leave all the countries on the EU’s external border [to fend for themselves], there will never be a common European asylum policy,” he said last week. “And if there is no common European asylum policy, there is a danger that uncontrolled immigration will once again take place throughout Europe.”

But calls for solidarity have repeatedly come up against the tough stance of rightwing anti-immigrant populists in Hungary and other EU states.

Even before Ankara launched its military offensive, the rate of arrivals on Greek shores was at its highest since March 2016, when a deal was struck between the EU and Turkey to deter people from making the sea crossing.

In less than three months, “irregular” migration has risen by 200%, according to Koumoutsakos, part of the centre-right government that took office in July. Last week alone, 1,563 people crossed from Turkey to the islands of Lesbos, Chios and Samos.

This year, almost 50,000 sea arrivals have been recorded in Greece, making it the main gateway to Europe for people fleeing wars and poverty in the Middle East, Africa and Asia.

Meanwhile, Erdoğan has angrily accused Brussels of failing to honour its commitments, including a pledge to give it €6bn in refugee aid.

Several EU states, including Greece, which views the 2016 agreement as the only effective way of dealing with the crisis, have signalled they will use the summit to press for Turkey to be given additional financial assistance. But it is a divisive issue and France has already voiced opposition.

For Greece’s prime minister, Kyriakos Mitsotakis, it will be a tough balancing act: while Athens advocates the need to fund Turkey further, it also wants it to be penalised for “provocative behaviour” in the eastern Mediterranean where Ankara is locked in a dispute with Cyprus over offshore drilling rights. EU leaders are likely to discuss possible sanctions.

Migration experts say time is of the essence. On Monday a fire broke out at an overcrowded camp above Vathy, the port town of Samos, after inter-ethnic clashes. Designed to host 650 people, the facility is accommodating nearly 6,000. Two weeks ago a blaze destroyed parts of Moria, a reception centre on Lesbos that is home to 13,842 people, four times over capacity.

“There is no question that Greece needs help,” said Gerald Knaus, director of the European Stability Initiative, a Berlin-based thinktank, and widely credited as the architect of the 2016 deal. The country, he said, was not only facing a backlog of 75,000 asylum claims, but was badly in need of caseworkers, interpreters and appeals panels to expedite the process of readmission to Turkey.

“A lot of what we are seeing is the result of the failure to decide claims quickly, “ he told the Guardian. He added that EU leaders could use the summit to create the post of an ombudsperson to monitor Turkey as a way of convincing Greek caseworkers it was a safe third country for families to return to.

Irrespective of the military incursion, Europe also had an interest in supporting Turkey, Knaus said. “While the EU will be critical of the invasion, it should also make clear that it is willing to support Turkey, especially in the event of another exodus from Idlib.”

Ankara has warned of as many as half a million more refugees streaming across Syria’s border into Turkey and on to Europe if Idlib falls. Tens of thousands of jihadists holed up in the region could be among them.

“The focus right now is on the offensive, but what is happening in Idlib is the big unknown,” said Knaus. “In many ways it worries me most.”