At a meeting with U.S. Deputy Assistant Secretary of Defense Jim MacDougall, Abiyev said the longstanding conflict over the Nagorno-Karabakh enclave poses a threat to the security of the Baku-Tbilisi-Ceyhan pipeline.
The pipeline is soon set to start delivering Caspian Sea oil to the Mediterranean.
According to a Defense Ministry statement, Abiyev said the Armenian leadership declared that it could recognize the independence of Nagorno-Karabakh. But he said if it does, it could lead to the resumption of fighting.
Armenia said last month that it could officially recognize Nagorno-Karabakh if negotiations on its status reach a dead end.
A 1994 cease-fire ended a six-year war that left Nagorno-Karabakh, a mainly ethnic Armenian enclave in Azerbaijan, in Armenian hands. Some 30,000 people were killed and 1 million displaced.
The region's self-declared independence is not recognized internationally.