A woman migrant has been found dead after shooting erupted as she and others tried to cross into Greece from Turkey by boat, Greek police told AFP on Sunday.

The incident occurred late on Saturday on the Evros River, some 67 kilometres (41 miles) northeast of the Greek city of Alexandroupolis, police said.

The woman was believed to have been aboard a boat carrying migrants who were trying to enter Greece from Turkey and ignored warnings from the Greek side to turn around.

"Last night a group of 10 people were found trying to cross into Greek territory by boat from the area of Soufli," a police spokesman in the region of Eastern Macedonia-Thrace told AFP.

"The Greek police signalled for them to stop but they did not obey. Shots were heard from the Turkish side. Greek border guards fired into the air to protect themselves," the spokesman said.  

"Greek border guards found four migrant men swimming ashore and a woman floating in the water who appeared to have been shot in the back around chest level", said the spokesman. 

An investigation has been opened into the incident. 

There was no immediate comment on the incident from the Turkish side.

According to Proto Thema newspaper website, the woman's wound indicates the gun that shot her was not one normally used by either Greek nor Turkish border police. 

Greece is often the country of choice for migrants fleeing war and poverty in Africa and the Middle East to try to reach a better life in the European Union.

After large numbers of migrants tried to cross the Evros River from Turkey in March 2020, Greece bolstered border patrols in the area and installed cameras, radar and a 40-kilometre (25-mile) steel fence over five metres (16 feet) high.