Turkish officials have said a man was fatally wounded when Greek security forces opened fire as migrants gathered at the border on Wednesday.
Greece immediately issued a flat denial, saying it was not involved in any such incident involving gunfire.
Thousands of people have headed to the border after Turkey said it would no longer stop migrants crossing.
Greece has also denied claims that two Syrians were fatally shot while trying to cross the border last night.
What happened at the border?
Videos taken close to Turkey’s northern border with Greece on Wednesday showed dozens of migrants hurrying through a field, escaping tear gas. Several men are seen carrying a man in a blanket as he held his head.
One of the men, speaking in Farsi, is heard on a video saying Greek soldiers had fired at their legs and that five migrants were wounded.
The local authority in the nearby town of Edirne then issued a statement saying one migrant had died in hospital and five had been wounded. It accused Greek police and border units of opening fire on migrants in no-man’s land between the Greek border gate at Kastanies and the Turkish gate at Pazakule.
Greek government spokesman Stelios Petsas was adamant there had been “no such incident with fire from the Greek authorities” and accused Turkey of “creating and spreading fake news”.
Three men from Afghanistan and Senegal have told the BBC’s Jonah Fisher of an earlier incident on Tuesday night in which they said they saw two Syrians fatally shot in the neck and head.
The men said it happened as they tried to cross the river which acts as a border at Ipsala, some 120km (75 miles) south of Edirne.
The River Evros is now heavily fortified, with Greek security forces every few metres, our correspondent reports.
Greek authorities told the BBC that no migrants had either been killed there or injured.