ATHENS (AFP) - Greece on Thursday rejected claims that its coastguard was responsible for the deaths of at least two migrants in the Aegean Sea when the boat carrying them to Europe capsized.

The UN refugee agency said Tuesday it has received eyewitness testimony that the boat carrying Afghan and Syrian migrants had capsized whilst being towed "at high speed" by a Greek coastguard vessel towards Turkish waters.

It has also urged Athens to investigate the weekend tragedy near the Greek island of Farmakonissi in which a woman and child were found dead, and nine others are still missing.

But Merchant Marine Minister Miltiades Varvitsiotis rejected the claims, telling state agency ANA: "When you have (rough) seas and (over 20) people on board a small fishing boat who are not familiar with the element, things are often difficult." The Greek coastguard on Wednesday denied pushing back the migrants towards Turkey. It said the boat had indeed been towed owing to bad weather, but in the direction of Greece, not Turkey.

The minister insisted that the coastguard follows EU regulations in intercepting undocumented immigrants.

The surviving migrants, who arrived in Athens on Thursday with UNHCR assistance, further charged that they were initially beaten off when they tried to climb onto the coastguard's vessel as their boat began sinking.

"The coastguards tried to push us back and hit us," Esanoullah Safi, a 38-year-old Afghan who lost his wife and four children in the incident, told AFP.

"They only allowed us on board when they saw that we were not letting go, and that a Turkish ship was closing in," he added.

Greece is one of the main ports of entry into the European Union for those fleeing war-torn and impoverished countries in Africa, the Middle East and the Indian subcontinent.

Refugee arrivals have soared over the past year because of the ongoing war in Syria. Arrivals by sea have also increased owing to stricter controls on the Greek-Turkish northern land border.

In November, German-based rights group ProAsyl had accused Greek authorities of pushing migrants back to Turkey in violation of international conventions.