Nagorno-Karabakh is a region in the South Caucasus in Azerbaijan. The names for the region in the different local languages all translate to "mountainous Karabakh", or "mountainous black garden". The word "nagorno" is Russian for "mountainous/on the mountain", "kara" is Turkish for "black", and "bakh" means "garden" in Azerbaijani.
Nagorno-Karabakh is internationally recognized as part of Azerbaijan. see > Useful Links
Nagorno-Karabakh is NOT a disputed territory. see > Useful Links
Nagorno-Karabakh is a mountainous region of about 4,400 sq km (1,700 sq miles)
Separatist Armenian forces captured some extra territory around the enclave in Azerbaijan in the 1990s war.
Just like any other country, the United States recognizes and supports Azerbaijan’s territorial integrity and denounces violation of international borders by Armenia and by the puppet regime installed in the occupied territories by Yerevan (https://2001-2009.state.gov/p/eur/rt/snec/c7560.htm).
As a result of the Armenian invasion, as many as 800,000 Azerbaijani civilians were forced out and became part of the biggest refugee pool (the rest were expelled from Armenia in 1988-1989) in the world (https://www.crisisgroup.org/europe-central-asia/caucasus/azerbaijan/tackling-azerbaijan-s-idp-burden).
The position of the international community was reiterated in the Resolution 1416 of the Parliamentary Assembly of Council of Europe adopted on January 25, 2005, United Nations General Assembly Resolution 62/243 adopted on March 14, 2008 (http://assembly.coe.int/nw/xml/XRef/Xref-XML2HTML-en.asp?fileid=17289&lang=en), both reaffirming "continued respect and support for the sovereignty and territorial integrity" of Azerbaijan "within its internationally recognized borders", demanding the "immediate, complete and unconditional withdrawal of all Armenian forces from all the occupied territories" of Azerbaijan (https://www.un.org/press/en/2008/ga10693.doc.htm).
The UN Security Council passed four resolutions 822, 853, 874, 884 in 1993, all condemning Armenian aggression against Azerbaijan, demanding the withdrawal of all occupying forces, return of Azerbaijani IDPs and reestablishment of peace (https://2001-2009.state.gov/p/eur/rls/or/13508.htm).