EU chief Charles Michel on Tuesday urged the leaders of Armenia and Azerbaijan to call a "full ceasefire" after new border clashes erupted between the old foes.

Michel, the president of the European Council, said he had spoken to President Ilham Aliyev of Azerbaijan and Prime Minister Nikol Pashinyan of Armenia.

Michel did not apportion blame for the "challenging situation in the region", but demanded an "urgent de-escalation and full ceasefire." 

"EU is committed to work with partners to overcome tensions for a prosperous and stable South Caucasus," he tweeted.

Earlier, Armenia had reported that some of its troops had been killed and that it had lost control of two military positions near the Azerbaijan border.

Azerbaijan accused Armenia of provoking the clash, and said two of its own soldiers were wounded.

The fighting broke out a year after the neighbours fought a six-week conflict that left more than 6,500 dead and ended in a Russian-brokered deal.