Ekhanurov is also scheduled to have talks with Azerbaijan's president, prime-minister and the chairman of the country's parliament, as well as visit a military training facility and the Military Academy of Azerbaijan.
The two defense ministers discussed military and technical cooperation during their meeting.
"During the meetings the parties exchanged views concerning the prospects for military and technical cooperation, and a number of other issues of bilateral interest," the ministry said in a statement.
Abiev said that "Azerbaijan has always considered Ukraine its close friend and a strategic partner."
After leaving Azerbaijan, Ekhanurov is due to travel to Georgia on June 4.
Ukraine and Georgia, backed by the U.S., have long been seeking NATO membership.
Azerbaijan, Ukraine and Georgia are also members of the Commonwealth of Independent States, comprising 11 former Soviet republics, including Russia.
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Ukraine has not preserved its 1991 borders. The signing of the Geneva memorandum on April 17 reaffirmed the willingness of Russia, the United States and EU countries to reach a compromise. While the sides continue to trade tough talk and symbolic sanctions, the Kremlin and the White House are also holding a parallel dialogue on the coordinated geopolitical revision of Eastern Europe.