"I asked the secretary general and the alliance, and member states to strengthen their presence... in the Aegean Sea with more ships," Mitsotakis said after talks with NATO chief Jens Stoltenberg.

"We ask... for the mission to be expanded to the south Aegean so we can cover the full scope of our country's maritime borders," he said, adding that he would raise the issue at a NATO summit in December.

Turkish President Recep Tayyip Erdogan earlier threatened that Ankara would allow millions of refugees to head to Europe if the bloc criticised Turkey's ongoing military offensive in Syria.

There are officially some 70,000 migrants and refugees in the country and scores continue to arrive daily, piling pressure on already overcrowded camps on the Greek islands.

NATO currently has six ships on patrol in the northern Aegean that track the movement of incoming migrant boats and alert the coastguards of Greece and Turkey, in addition to EU border force Frontex.

Stoltenberg said he has already called on allies to provide more ships, but that any additional commitment requires a consensus between NATO members.

"We are sharing information. It's not our mandate to stop the boats," he said.