Azerbaijan's defence ministry says it has begun "anti-terrorist" operations in its breakaway region of Nagorno-Karabakh, under Armenian control.
Tensions have been high for months surrounding the ethnic Armenian enclave, recognised internationally as part of Azerbaijan.
Eleven Azerbaijani police and civilians have been reported killed in a mine blast and another incident.
Air raid sirens have been reported in Karabakh's main city.
The two neighbours, Azerbaijan and Armenia, have gone to war twice over Nagorno-Karabakh, first in the early 1990s after the fall of the Soviet Union and again in 2020.
Since December, Azerbaijan has mounted a de facto blockade of the only route into the enclave from Armenia, known as the Lachin Corridor.
On Tuesday, the defence ministry in Baku accused Armenian forces of "systematic shelling" of army positions and said it had responded by launching "local, anti-terrorist activities... to disarm and secure the withdrawal of formations of Armenia's armed forces from our territories".
It insisted it was not targeting civilians or civilian facilities, but instead said "only legitimate military targets are being incapacitated by the use of high-precision weapons".
Armenia's defence ministry said the claims of Armenian fire did not correspond with reality.