Nassirov told journalists on the sidelines of an annual Caspian Oil and Gas conference that the country had already applied for the resumption of exports.
He said oil export volumes in July were expected to be 80,000 tonnes, with a further increase in the following months.
SOCAR stopped supplies to Russia's Black Sea's port of Novorossiisk in March, saying planned maintenance on the Baku-Novorossiisk pipeline started on March 1, and cancelled the loading of two 80,000-tonne cargoes.
The company diverted crude flows to its own Baku-Tbilisi-Ceyhan pipeline after the suspension of transit via Russia.
Oil exports via Russia in the first two months of this year totalled 164,800 tonnes.