Greek President Karolos Papoulias has cut short a visit to neighbour Albania, after a minority group's protest which Athens described as disruptive.
The Chams say they were badly treated by Greece
Up to 200 demonstrators from the Albanian Muslim Cham clan gathered outside a hotel where Mr Papoulias was due to meet counterpart Alfred Moisiu.
The Greek foreign ministry said Albania had not taken steps to ensure a trouble-free meeting.
Albania said the protest was peaceful and Greece's decision unjustified.
"We express our deep regret after this hasty and unexplained decision of the Greek delegation, based on misinformation despite assurances given by the Albanian side," said presidential spokesman Aferdita Sokoli.
The two presidents were due to meet in the southern Albanian town of Sarande, opposite the Greek island of Corfu, on Tuesday afternoon.
But Mr Papoulias waited at a Greek consulate in another town, Gjirokaster, after hearing about the protest, and left for home when demonstrators failed to disperse.
"The Albanian authorities... did not take measures to deter known extreme elements, who in their effort to block the smooth development of the countries' ties present unacceptable, non-existent issues at a time when Albania is taking steps towards completing its European expectations," a Greek foreign ministry statement said.
Around 35,000 Chams were expelled from Greece after World War II after being accused of collaboration with the Nazi occupation, they say. They were given Albanian citizenship in 1953.
The demonstrators, carrying banners reading "We want justice" and "Stop the indifference", were demanding compensation for or restitution of properties confiscated by the Greek government.
"We want basic rights. That is our land, our property. We thank the Albanian people for keeping us until now but we want to be back at our land," demonstrator Rexhep Ceno told AP news agency.
Albanian officials and local media said the demonstration was peaceful and under police control.