The July 22 call with Armenian Foreign Minister Zohrab Mnatsakanian and his Azerbaijani counterpart Ceyhun Bayramov was the first such direct diplomacy that brought the three together simultaneously.
Borell called on both sides to commit to a cease-fire and take immediate action to deescalate the situation.
The EU’s top diplomat “urged both sides to stop the armed confrontation and to refrain from action and rhetoric that provoke tension, in particular from any further threats to critical infrastructure in the region,” the European Union External Action service said in a statement.
Separately on July 22, UN Secretary-General Antonio Guterres called for “immediate and full deescalation” and “a return to negotiations” between Azerbaijan and Armenia.
Guterres spoke by telephone separately with Azerbaijan President Ilham Aliyev and Armenian Prime Minister Nikol Pashinian.
Fighting between the neighboring South Caucasus countries has killed at least 12 Azerbaijani soldiers, including a general, and four Armenian servicemen since a flare-up of violence began on July 12 that lasted several days.
Each side has blamed the other for starting the fighting, the worst outbreak of violence in the region since clashes in Nagorno-Karabakh in 2016.
Armenia and Azerbaijan fought a war over Nagorno-Karabakh in the late 1980s and early 1990s as they transitioned into independent countries amid the dissolution of the Soviet Union. About 30,000 people were killed.
Nagorno-Karabakh is internationally recognized as part of Azerbaijan but is controlled by Armenian separatists.
The Organization for Security and Cooperation in Europe (OSCE) is urging the sides to resume peace talks. Both Washington and Moscow have called on the countries to halt the violence immediately.
With reporting by AFP