Friday's skirmish violating the brittle truce comes a day after the Organization for Security and Cooperation in Europe said that the presidents of the two feuding nations were ready to "meet each other later this year" in an effort to end years of hostility.
Azerbaijan and Armenia have been locked in a dispute over the separatist Nagorny Karabakh region since a bloody war in the early 1990s following the breakup of the Soviet Union.
"On July 24, Armenian army units shelled Azerbaijani positions" at the Karabakh frontline and the Azerbaijani-Armenian state border, the defense ministry in Baku said in a statement reported by AFP.
One Azeri serviceman was killed in crossfire, said the defense ministry, claiming that at least five Armenian troops were killed in the clash.
Armenia denied that it had sustained any casualties and accused Azerbaijan of violating a 1994 ceasefire.
"Some 160 violations have been registered over the past night," Armenian defense ministry spokesman Artsrun Hovannisyan told AFP. "Armenia's armed forces returned fire."
On Thursday, the OSCE Minsk Group, which is involved in the efforts to find a diplomatic solution to the conflict, said Armenian President Serzh Sarkisian and his counterpart from Azerbaijan Ilham Aliyev were ready to meet each other later this year.
The statement was released after the group's Russian, US and French co-chairs travelled to Yerevan and Baku for meetings with the warring countries' leaders.
"They instructed their foreign ministers to continue their work with the co-chairs on an agenda for the presidential summit," the OSCE Minsk Group said.
Officials in Armenia and Azerbaijan did not confirm the statement, however.