Wednesday’s incident is the latest in a series of skirmishes between troops of the two former Soviet republics in recent months.
Several lives have already been lost this year, leaving the decade-old ceasefire between the two sides increasingly fragile.
The shootings forced the Organisation for Security and Co-operation in Europe’s special envoy, Andrzej Kasprzyk, to abandon a visit to monitor the ceasefire, according to the Azeri defence ministry.
In a statement, the ministry said the clash happened near the village of Agdam in the Tovuz region of north-western Azerbaijan. It said Azeri troops returned fire and suffered no casualties.
However, neither OSCE or the Armenian government were prepared to comment on the Azeri statement.
Ilham Aliyev, widely seen as Azerbaijan's president-in-waiting, has ruled out any compromise with Armenia in the bitter conflict.
In an interview in the Friday edition of Russia's Izvestia daily, the son of ailing president Haydar Aliyev said the only acceptable solution to the protracted dispute was "the total liberation of the territory which Armenian forces have occupied".
"Until our territories are
liberated we will not have any cooperation with Armenia"
Azeri president's son
And he excluded any resumption of normal trade with
Azerbaijan's neighbour, saying: "Until our territories are
liberated we will not have any cooperation with Armenia."
The territory has been in dispute for decades, but renewed ethnic conflict erupted there in 1989 during the dying days of the Soviet Union.
Azeri forces were driven out and ethnic Armenians have since
established self-government in the region.
Balance of power
In a complicated history of forced relocations, wars and resettlement – spread over 120 years - a war of secession from Azerbaijan ended in a ceasefire in 1994.
Most of the enclave came under the de facto control of Armenia – but there has been no international border agreement.
The fighting displaced about a million people from their homes and left tens of thousands dead on both sides.
The two countries remain on high alert, with a permanent peace settlement proving elusive.
Western governments are wary that conflict could destabilize the Caucasus region, soon to become a major crossroads for oil exports from the Caspian Sea to world markets.