Armenia and Azerbaijan on Thursday said they had agreed to sign a peace deal after decades of conflict, with Armenia agreeing to surrender its claim over the primarily Armenian-populated Karabakh region.

Azerbaijan and Armenia have agreed on a draft text of a peace agreement, Azeri Foreign Minister Ceyhun Bayramov announced on Thursday. Bayramov said that Armenia has accepted Azerbaijan's proposals regarding the last remaining disputed points in the deal, though he did not specify what those were.

Armenia and Azerbaijan were locked in conflict over Nagorno-Karabakh for nearly four decades after the Soviet Union they were both members of collapsed.

But hurdles remain. Azerbaijan also said Armenia’s constitution must “eliminate the claims against the sovereignty and territorial integrity of Azerbaijan,” as a prerequisite to allow for the signing of the peace treaty.

Armenia and Azerbaijan have fought a series of wars since the late 1980s, when Nagorno-Karabakh, a region in Azerbaijan that had a mostly Armenian population at the time, broke away from Baku with Yerevan's support.