Video report by ITV News Correspondent John Ray
If true, the downing of a fighter jet by Azerbaijan's ally Turkey could escalate tensions.
Both Turkey and Azerbaijan have denied the claim.
Armenian officials said an SU-25 from its air force was shot down in Armenian airspace by a Turkish F-16 fighter jet that took off from Azerbaijan, and the pilot was killed.
Turky has dismissed the allegation as "absolutely untrue" while Azerbaijani officials called it "another fantasy of the Armenian military propaganda machine."
Earlier on Tuesday, Azerbaijan’s Defense Ministry accused Armenian forces of shelling the Dashkesan region in Azerbaijan.
But Armenian officials said it was Azerbaijani forces that had opened fire on a military unit in the Armenian town of Vardenis - setting a bus on fire and killing one civilian.
Armenia's Foreign Ministry denied shelling the region and said the reports were laying the groundwork for Azerbaijan "expanding the geography of hostilities, including the aggression against the Republic of Armenia."
Dozens of people have been killed and wounded since fighting broke out Sunday.
The Nagorno-Karabakh Defense Ministry reported 84 servicemen killed, while Azerbaijan President Ilham Aliyev said 10 civilians were killed on its side, he didn’t detail the country’s military casualties.
Why is there fighting over the disputed region?
Nagorno-Karabakh lies within Azerbaijan but has been under the control of ethnic Armenian forces backed by the Armenian government since 1994 at the end of a separatist war following the breakup of the Soviet Union three years earlier.
Mostly mountainous Nagorno-Karabakh - a region some 1,700 square miles - lies 30 miles (50km) from the Armenian border.
Local soldiers backed by Armenia also occupy some Azerbaijani territory outside the region.
Turkey supports Azerbaijan in the conflict, with President Recep Tayyip Erdogan urging Armenia to withdraw immediately from the separatist region.
International efforts to settle the conflict have stalled and fighting sporadically breaks out.
In July, one of the most severe outbreaks of fighting in years left 16 people from both sides dead.