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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The self-defense forces in Donbass likely do not have the capability to win. Kiev will simply outlast the republic’s fighters. Ukraine still has many mobilization resources. The most important thing for self-defense fighters is not to win the war but rather not to lose it.