In a statement, Russia said the two countries' foreign ministers agreed in a phone call on Monday to speed up work on the agreement, which was at "a high stage of readiness".
The Russian foreign ministry did not detail the scope of the agreement, which comes amid growing political, trade and military ties between Moscow and Tehran that the United States views with concern, Reuters reported.
Last week President Vladimir Putin held five hours of talks in the Kremlin with Iranian President Ebrahim Rawisi.
Amirabdollahian and his Russian counterpart Sergey Lavrov discussed bilateral ties and regional issues including the latest developments regarding the Israeli war on Gaza and in the West Bank during a telephone conversation on Monday.
During the telephone conversation, the Russian foreign minister also described the meeting between Iranian President Ebrahim Raeisi and his Russian counterpart Vladimir Putin as highly significant.
MNA