Armenia's Prime Minister Nikol Pashinyan talked with the French and Russian presidents and the US Secretary of State, after "provocative, aggressive actions" by Azerbaijan, his office said on Tuesday.
In his phone calls, Mr Pashinyan "emphasised the importance of adequate reaction from the international community".
Azerbaijani troops have been killed in large-scale clashes on the border with Armenia after the latest flare-up between the countries.
Since the end of the 2020 war between Yerevan and Baku over the contested Nagorno-Karabakh region, there have been frequent reports of shootouts along their shared border.
"At 00.05am on Tuesday, Azerbaijan launched intensive shelling, with artillery and large-calibre firearms, against Armenian military positions in the direction of the cities of Goris, Sotk and Jermuk," Armenia's Defence Ministry said.
It said Azerbaijan had also used drones.
But Azerbaijan's Defence Ministry accused Armenia of "large-scale subversive acts" near the districts of Dashkesan, Kelbajar and Lachin on the border.
It said its army sites "came under fire, including from trench mortars".
"There are losses among [Azerbaijani] servicemen," it said, without giving figures.
US Secretary of State Antony Blinken appealed for an end to the fighting.
“The United States is deeply concerned about reports of attacks along the Armenia-Azerbaijan border, including reported strikes against settlements and civilian infrastructure inside Armenia,” Mr Blinken said in a statement on Monday on the State Department’s website. “We urge an end to any military hostilities immediately.”
Last week, Armenia accused Azerbaijan of killing one of its soldiers in a border shootout.
In August, Azerbaijan said it had lost a soldier and the Karabakh army said two of its troops had been killed and more than a dozen injured.
The neighbours fought two wars — in the 1990s and in 2020 — over the Nagorno-Karabakh region, Azerbaijan's Armenian-populated enclave.
Six weeks of fighting in the autumn of 2020 killed more than 6,500 people and ended with a Russian-brokered ceasefire.
Under the deal, Armenia gave up large areas of territory it controlled for decades and Moscow posted about 2,000 Russian peacekeepers to oversee the fragile truce.
During EU-mediated talks in Brussels in May and April, Azerbaijani President Ilham Aliyev and Mr Pashinyan agreed to "advance discussions" on a future peace treaty.
Ethnic Armenian separatists in Nagorno-Karabakh broke away from Azerbaijan when the Soviet Union collapsed in 1991. The ensuing conflict killed about 30,000 people.