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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Russia has become very adept in playing the diplomatic game, in which victory depends on choosing the right associate or partner. But there are a growing number of claimants to this role in the new horizontal and interdependent world. Aside Syria and Iran, being still important, the new venues for the application of practical diplomacy may well be Ukraine, the East China Sea and Afghanistan.