Prior to the war of 2020 it seems like Nagorno-Karabakh remained recognized as Azerbaijani territory by most international organizations. Does this remain the case after the war? Have there been any official statements since the war on who has legal rights to Nagorno-Karabakh?
The position of the West expressed during and after the 2020 war is that the two sides should negotiate under the auspices of the Organization for Security and Co-operation in Europe (OSCE), and reach a mutually agreed settlement. The US and UK have not stated exactly what settlement they wish to see.
In November 2020, the UK government stated its position in a message to the OSCE, which is that a settlement should be negotiated between the belligerents at negotiations organised by the OSCE, through a structure known as the The OSCE Minsk Group.
The UK would like to reiterate its support for the OSCE Minsk Group as the primary format through which any final settlement is reached.
On October 8, the US issued a similar statement, calling for a ceasefire and negotiated settlement under the auspices of the Minsk Group.
Hence rather than taking a position on what form the final status of Nagorno-Karabakh should be, they would prefer the parties to negotiate a fair agreement under international guidance.