BAKU, AZERBAIJAN—During peace talks over the long-disputed territory of Nagorno-Karabakh, officials from both Armenia and Azerbaijan announced Monday they would only agree to a ceasefire if it included a provision that allowed them to continue shooting missiles at each other. “After decades of conflict, I truly believe we are on the verge of a diplomatic breakthrough, so long as any agreement to pause hostilities recognizes our absolute right to launch ballistic missiles and carry out bombing raids against our adversary,” Azeri President Ilhan Aliyev said in a statement that was echoed by Armenian authorities and followed days of negotiations for which refusing to stop missile strikes and the shelling of civilian residences was a strict precondition. “We’ve been able to find common ground on many issues, especially the need for any truce to include language that preserves the ability of each side to fire explosive devices at the other. That’s nonnegotiable, of course. Once we have a ceasefire in place, it is my hope we will sign a permanent treaty that allows us to lay down our arms and, apart from the occasional incineration of an entire village, live in peace.” Both Armenia and Azerbaijan reassured the international community that during a ceasefire the use of all other weapons, including guns and hand grenades, would be strictly limited to close-quarter combat situations in which missiles weren’t an option.