The mainly Armenian-populated enclave broke away from Muslim Azerbaijan with the backing of Christian Armenia as the Soviet Union collapsed.
Since then, Nagorno-Karabakh has run its own affairs with heavy financial and military support from Yerevan.
The last two years have seen the worst skirmishes since a 1994 ceasefire, raising fears of a return to full-blown conflict in the South Caucasus, an important route for oil and gas supplies from the Caspian region to Europe.
In a statement issued after visiting the region, mediators from the Organisation for Security and Cooperation in Europe (OSCE) expressed concern that the planned opening of an airport in May "could lead to further increased tensions".
"The Co-Chairs urged the sides to reach an understanding in keeping with international conventions and agreements," the OSCE Minsk Group of French, U.S. and Russian envoys said in a statement.
Azerbaijan, its military budget bloated by oil and gas sales, had threatened to shoot down planes landing at the airport, but has since toned down its rhetoric. Armenian President Serzh Sarksyan says he plans to be on the first flight, tentatively scheduled for May 9.
Azerbaijan hosts oil majors including BP, Chevron and ExxonMobil.
The airport was heavily damaged and closed by the war, in which Armenian-backed forces seized control of Nagorno-Karabakh and seven surrounding Azeri districts forming a land corridor with Armenia.
Rebuilt at a cost of $3 million, it will have regular flights between Yerevan and the enclave, currently a five-hour drive apart along a single road snaking through mountains.
Though not recognised as independent by any country, Nagorno-Karabakh is seeking to garner the trappings of statehood, an airport among them. Azerbaijan says this prejudices negotiations that have failed for the past 16 years to produce a peace settlement.
The OSCE statement said the mediators "cautioned that the operation of flights to and from this airport could not be used to support any claim of a change in the current state of Nagorno-Karabakh under international law".