"The joint exercises...are designed to develop procedures for protecting offshore oil fields from terrorist attacks," Abbiyev told journalists, adding that they started Wednesday and would continue for several days.
The minister did not comment on what form the exercises would take, or the level of participation on the US side.
Azerbaijan's sector of the Caspian Sea has substantial oil wealth, and western companies including BP, ExxonMobil, ChevronTexaco and ConocoPhillips are partners in several oil field consortiums there.
Western companies, with backing from Washington, are also building a pipeline which will pump crude oil from the landlocked Caspian Sea, via Azerbaijan, Georgia and Turkey, to world markets.
Wednesday's exercises were part of a 4.4-million-dollar (3.89-million-euro) military aid package to Azerbaijan announced last year by the US government and aimed at improving the former Soviet republic's maritime security.
That aid has been interpreted as a coded warning to neighbouring Iran, which disputes Azerbaijan's borders in the Caspian Sea and claims it is the rightful owner of the Azeri Alov-Sharg-Araz oil prospect.
In the summer of 2001, an Iranian warship threatened to fire on an Azeri research vessel prospecting for oil on the disputed field.
The United States has tense relations with Iran and President George W. Bush has designated the country part of an "axis of evil."