Turkey's coastguard said on Monday it had rescued 35 migrants and was searching for four more missing from a boat found half sunken in the Aegean Sea.
The Turkish coastguard quoted the rescued migrants as saying that Greek coastguards had slashed their rubber dinghy, taken away their fuel containers, and pushed them back towards Turkish waters. A Greek coastguard spokesman denied the allegations.
"The migrant boat never entered Greek territorial waters," the Greek spokesman told Reuters. "There was never any contact between a Greek coastguard ship and the migrants' boat."
The migrants were rescued around 2:45 am (2345 GMT) near a small island off the coast of Ayvalik in Turkey's western Balikesir province, the Turkish coastguard said.
Greece has been one of the main gateways into the European Union for people fleeing conflict in the Middle East and beyond, largely via its islands near the Turkish coast.
More than a million people reached Greece from Turkey in 2015-16, although the numbers later dropped sharply under a 2016 agreement between the EU and Turkey for Ankara to take migrants back in return for funds.
Earlier this year, tens of thousands of migrants tried to cross into Greece via land and sea borders after Ankara said it would no longer stop them. Turkey, home to 3.6 million Syrians, the world's largest refugee population, had said it would open the frontier because it was alarmed by the prospect of another wave of refugees fleeing war in northwest Syria.