Mohammad Javad Zarif made the comments at a telephone conversation with his Armenian counterpart Eduard Nalbandian.
He said Iran is ready to play a role in the settlement of the crisis if the two warring sides want so.
Zarif once again called for the cessation of hostilities and for restoration of peace to the region.
The top Iranian diplomat is also going to meet his Azeri counterpart on Tuesday at a counter-terrorism meeting in Iran’s northern city of Ramsar.
Iran has repeatedly called on Baku and Yerevan in recent days to show restraint and start peaceful negotiations instead of military confrontation.
At least 30 soldiers have been killed in fighting between Armenian and Azerbaijani forces along the frontlines of the Nagorno-Karabakh region. Each side blames the other for the fighting.
Nagorno-Karabakh has been under the control of Armenian military and separatists since a war between Armenia and Azerbaijan ended in 1994. Years of negotiations have brought little progress in resolving the dispute.
Fighting on Saturday marked the worst clashes since 1994, said David Babayan, spokesman for the region's separatist president.