Thousands of ethnic Armenians fled the breakaway region of Nagorno-Karabakh by Monday after their fighters were defeated by Azerbaijan.
Azerbaijan says it will guarantee their rights and integrate the region but the leadership of the Armenians in Karabakh stated that they would leave.
The Armenians of Karabakh, which is internationally recognized as part of Azerbaijan, were forced to declare a ceasefire earlier this week.
Azerbaijan claimed it was carrying out anti-terrorist activities after a mine killed six people in the contested Nagorno-Karabakh.
There appeared to be no immediate response to the offer from Azerbaijan.
Russia has maintained peacekeepers in the region since a 2020 war in which Azerbaijan seized back significant amounts of territory it had lost to Armenian forces in the 1990s.
In recent months, Russia has publicly backed Azerbaijan's claim to Nagorno-Karabakh and blamed Armenia for the ongoing blockade of separatist-held Karabakh.
Armenia and Azerbaijan have fought two wars in the past 30 years over Nagorno-Karabakh.
The main corridor connecting Armenia and the Nagorno-Karabakh region has been restricted or blocked since December.
The reported strikes in the Nagorno-Karabakh region come as Armenia and Azerbaijan conduct peace talks in the US.