Greek Prime Minister Kyriakos Mitsotakis on Sunday announced a new scheme to protect unaccompanied migrant minors reaching the country, two days after condemning other EU states for their lack of solidarity.

The prime minister's office will take charge of the new "No Child Alone" programme, which he said was designed to protect unaccompanied children from "exploitation and criminality".

Referring to the need to protect unaccompanied child migrants arriving in Greece, he said in a statement: "There is a wound of the migrant crisis that we can heal immediately by ourselves.

"Our civilisation, our humanity, our sensitivity and tradition dictates that we do so." Mitsotakis pledged to quickly settle 4,000 children living on Greece's Aegean islands in "miserable conditions" to accommodation where, he said, "they will live and be fed as dictated by their tender age".

On Friday, he told deputies he had failed to persuade other EU states to accept around 3,000 unaccompanied minors. "We attempted to reach agreement with all EU states, saying 'for God's sake, we are talking about 3,000 children... can they not be shared out among 27 countries so that Europe can show solidarity?'," he said.

"Unfortunately, I regret to say the reply was not positive, and it does not do Europe justice," he added.

Greece's conservative government this week announced a plan to massively overhaul its overcrowded migrant camps on the Aegean islands facing Turkey.

They also said they would work to make the borders 'air-tight' against a feared new surge of asylum-seekers.

According to government figures, there are over 37,000 asylum-seekers on the islands, with hundreds more arriving daily, capitalising on mild weather conditions.

A total of 643 migrants and refugees arrived with boats Saturday on the Aegean islands.

The Greek coast guard rescued another 60 people in two incidents in the seas off the islands of Lesbos and Samos.

The International Organisation for Migration says there are an additional 22,000 people in camps on the mainland, which are nearly full or already past capacity.

On the island of Samos, a local mayor this week threatened to resign in protest at plans for a new camp to house at least 5,000 people.

There have also been protests in several towns in northern Greece in recent weeks to block attempted relocations of asylum-seekers.

Mitsotakis this week accused the European Union of treating countries on the bloc's external frontiers as convenient places to park migrants.