In a statement on Wednesday, Azerbaijan's Defence Ministry said that seven soldiers were killed, and 10 others wounded in the clashes on Tuesday, reports Xinhua news agency.
Meanwhile, the Armenian Defence Ministry said one soldier was killed, and 24 others were reportedly missing in the clashes, adding that troops were captured by Azerbaijani forces.
Two Armenian military positions were taken by the Azerbaijani side, it further claimed.
Both sides have accused each other of launching provocative attacks.
Hours after the clashes, the two countries reached a Russia-brokered ceasefire agreement.
Both confirmed on Wednesday that the clashes had stopped, and that the border situation was stable since the ceasefire.
The last round of major armed clashes between the two South Caucasian countries over the disputed territory of Nagorno-Karabakh broke out in September last year, that claimed the loves of more than 6,000 people.
It ended with a Russia-brokered truce in November 2020.
Some 2,000 Russian peacekeepers were deployed to patrol the area in and around Nagorno-Karabakh.