Speaking in Armenia, she warned that the clashes “could escalate into a considerably broader conflict” in the Caucasus.
The two former Soviet republics fought a bloody war over the disputed region of Nagorno-Karabakh in the 1990s. A formal ceasefire is now looking increasingly fragile.
“I am quite concerned by these incidents and have referred to as on all parties, all actors, to refrain from the use or threat of force,” Mrs Clinton stated after her talks in the Armenian capital, Yerevan, on Monday.
“There is a danger that it could escalate into a significantly broader conflict that would be very tragic for everyone concerned,” she warned.
The BBC’s Damien McGuinness, in neighbouring Georgia, says it is hoped Mrs Clinton will ease tensions among the two countries.
The region is dependent on US aid, so Washington has considerably influence there, he says.
The conflict between Armenia and Azerbaijan erupted as the Soviet Union collapsed and at least 30,000 individuals had been killed by the time the truce was declared in 1994.