A child has died and another has been hospitalised after a makeshift boat packed with dozens of refugees and migrants capsized off the coast of Lesbos, Greek port police said.

One young boy could not be revived after being found "unconscious", the Greek coastguard said in a statement on Monday, while the other was taken to hospital and is now considered out of danger. A further 46 people are safe following the rescue.

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Greece's coastguard alleged that the occupants of the boat deliberately overturned it as a coastguard vessel approached.

"The coastguards' account of this encounter is that the vessel, a rubber dinghy, approached the maritime border line accompanied by a Turkish coastguard vessel, which then turned away once they had ensured the vessel had entered Greek waters," said Al Jazeera's John Psaropoulos, reporting from Lesbos.

In a statement on Sunday, Greek government spokesman Stelios Petsas alleged Turkey had been encouraging people to test the Greek border.

"Instead of curtailing networks of people smugglers, Turkey has itself become a smuggler," said Petsas.

Thousands of refugees and migrants are trying to find a way across Turkey's western border with Greece, with only dozens managing to pass through either border fences or crossing the river that runs along the frontier.

At least 1,000 refugees and migrants have reached Greece's Eastern Aegean islands since Sunday morning, a police official told Reuters news agency.

This comes after Turkey opened its side of the frontier to refugees and migrants to leave the country for Europe. Others are trying to reach Greek islands from the Turkish coast.

Turkey declared its borders open amid a Russia-backed Syrian government offensive into Syria's northwestern Idlib province.

"It is a very large increase compared with usual inflows," reported Psaropoulos.

"People here on the island have been getting very nervous about whether that will continue - and some people have been showing persistent determination and resolve to prevent the authorities from doing what they normally do, which is search-and-rescue at sea and resupply of the camp at Moria.

"They have been blocking the roads to the camp - to camera crews, all journalists, to the authorities and also to any who have any work at the camp. This is the attitude we have seen on the island in the past 24 hours."

Greece's prime minister also announced he was freezing asylum applications following a meeting of the National Security Council on Sunday.

"As of now, we will not be accepting any new asylum applications for one month," Kyriakos Mitsotakis tweeted. Greece is currently processing 125,000 applications and appeals.

Greece is invoking Article 78 of the Treaty on the Functioning of the European Union, which allows the EU to provide Athens with assistance in an "emergency situation characterised by a sudden inflow of nationals of third countries".

A deal was reached between the European Union and Turkey after a crisis in 2015 saw waves of refugees arriving on Europe's shores, many who remain in Turkey.

The deal calls for the EU to pay a total of six billion euros ($6.7bn) to help Turkey accommodate the crowds and hold them back from EU borders. So far, 3.2 billion euros ($3.6bn) have already been paid out, a spokesman for German Chancellor Angela Merkel said on Monday.

Turkey now hosts some four million refugees - the majority of them Syrians - but has called for the EU to provide additional support for hosting them.

A fresh surge of migrants has arrived on its border with Greece in recent days after an escalation of fighting in Syria's Iblib province between Turkey and Russian-backed Syrian forces.

Turkey's President Recep Tayyip Erdogan has warned he no longer feels bound by the agreement and had opened the country's borders to the EU.

"After we opened the doors, there were multiple calls saying 'close the doors'. I told them 'it's done. It's finished. The doors are now open. Now, you will have to take your share of the burden'," he said on Monday.

"Hundreds of thousands have crossed, soon it will reach millions," he said. But the numbers remain in dispute.

Erdogan also said he hoped to reach a deal on a ceasefire in Syria when he meets his Russian counterpart Vladimir Putin on Thursday, following intense fighting in the last opposition holdout of Idlib.