Azerbaijan denies the accusation from Armenia. France, Russia and the US have urged the two countries, which fought a deadly war last year, to de-escalate.
Armenian leader Nikol Pashinyan on Thursday accused Azerbaijani troops of crossing into the country in a new escalation of tensions months after a deadly eruption of violence over Nagorno-Karabakh.
"This is a subversive infiltration," Pashinyan told an extraordinary meeting of his security council, according to an official statement.
He accused Azerbaijan of trying to "lay siege" to Lake Sev, which is shared by the two countries, and said the country's army had responded to the "encroachment" with "appropriate tactical maneuvres".
Baku rejected the accusations as "provocative" with the Foreign Ministry stating: "The border guards are taking up positions that belong to Azerbaijan in the Lachin and Kalbajar districts."
Azerbaijan, it added, "is committed to easing tensions in the region and calls for measures in this direction."
French President Emmanuel Macron has called on Azerbaijani troops "to withdraw immediately".
France co-chairs the Minsk Group, alongside the US and Russia, which aims to find a peaceful solution to the conflict between the two countries over the region of Nagorno-Karrabakh.
Washington has they are "closely following" the situation.
"We understand communication between the parties is ongoing and urge restraint in de-escalating the situation peacefully," the Department of State spokesperson, Ned Price, said on Twitter.
The Kremlin said Vladimir Putin "emphasised the need to strictly abide" to the truce agreement struck in November during a phone call on Friday morning with Pashinyan.
"The President of Russia reaffirmed Russia's commitment to further active mediation and close contacts with Yerevan and Baku in the interests of ensuring stability in the region," the statement also said.
The Russian Foreign Ministry had said earlier that Sergey Lavrov had spoken by phone with his Azerbaijani counterpart Jeyhoun Baeramov about "the deterioration of the situation".
Moscow's readout of the call says the two ministers stressed the "need for strict observance of the ceasefire"
Tensions between the two countries have been simmering since the end of a war in the 1990s over Nagorno-Karabakh.
Last year's flare-up was the most violent observed in decades with the 44-day conflict leaving 5,000 people dead and tens of thousands displaced.
It ended in November with a Russian-brokered truce which saw Armenia forced to cede significant territory to Azerbaijan, which in turn sparked calls for a significant political upheaval in Yerevan.