Since its origins in the ninth century, Dadivank Monastery has withstood Seljuk and Mongol invasions, Persian domination, Soviet rule and, this fall, a second brutal war between Armenia and Azerbaijan. Now the majestic stone complex — which includes two frescoed churches, a bell tower and numerous medieval inscriptions — faces something that could be even worse: a dangerous peace.

Perched on a rugged slope west of Nagorno-Karabakh, Dadivank is one of the hundreds of Armenian churches, monuments and carved memorial stones in a disputed region that will come under the control of predominantly Muslim Azerbaijan according to a cease-fire agreement reached this month. Some of those structures — like the Amaras monastery and the basilica of Tsitsernavank — date to the earliest centuries of Christianity. For many Armenians, turning over so much of their heritage to a sworn enemy poses a grave new threat, even as the bloodshed has for the moment come to an end.

Their concern is understandable. Under the cease-fire, hundreds of thousands of Azerbaijanis uprooted by a previous war in the early 1990s will be able to return. In a victory speech on Nov. 25, President Ilham Aliyev of Azerbaijan suggested that Armenians have no historical claims to the region, asserting that the churches belonged to ancient Azerbaijani forebears and had been “Armenianized” in the 19th century.

Between 1997 and 2006, the Azerbaijani government undertook a devastating campaign against Armenian heritage in Nakhichevan, an Azerbaijani enclave separated from the main part of the country by Armenian territory: Some 89 churches and the thousands of khachkars, or carved memorial stones, of the Djulfa cemetery, the largest medieval Armenian cemetery in the world, were destroyed. And since the recent cease-fire, images circulating on social media suggest that some Armenian monuments and churches in territory newly claimed by Azerbaijan have already been vandalized or defiled.

On the other hand, Armenian forces laid to waste the Azerbaijani town of Agdam in the wake of the previous Nagorno-Karabakh war in the 1990s. The Azerbaijani government has also claimed that mosques and Muslim sites that had been under Armenian control were neglected or desecrated.

Now, as Azerbaijan takes possession of newly won territories, a longstanding problem acquires special urgency: How can a government be persuaded to care for the heritage of a people that doesn’t fit into its view of the nation?