Iran also reported that a military helicopter had crashed in the region, killing at least one of eight people on board.
"This morning while on a mission in the northwestern province of West Azerbaijan the commander Saeed Ghahari was martyred in a helicopter crash," the semi-official Fars news agency Fars said without giving a source.
Firat, a Kurdish news agency based in Brussels, said that the Party of Free Life of Kurdistan (PJAK), an Iranian offshoot of the Kurdistan Workers Party (PKK), claimed to have shot down the helicopter with a shoulder-held missile, killing eight soldiers and capturing one.
Iran said the guards were continuing "to fully clean up the region of anti-revolutionary elements," without giving further details about the fighters.
The report said that the commander of the ground force carrying out the operation had an "accident due to bad weather" while flying by helicopter with eight others to check on the area, but did not say if there were casualties.
Iran's northwestern West Azarbaijan province, which has borders with Turkey and Iraq, has already been the scene of regular armed clashes between Iranian border guards and Kurdish fighters, in particular Pejak, a group linked to Turkey's outlawed Kurdistan Workers' Party (PKK).
Turkey has praised Iran's efforts to crack down on Kurdish rebels who have been waging a deadly armed struggle for self-rule in the southeast of Turkey since 1984.
Iran is bound by treaty with Turkey to fight the PKK.
In return, Turkey has pledged to fight the outlawed Iranian armed opposition group, the Iraq-based People's Mujahedeen.
Iranian media reports said in December that police had arrested 87 members and supporters of "terrorist groups" and killed nine in West Azarbaijan province over a 10 month period.
In November, Iran said it arrested four men with links to Kurdish fighters who it said were plotting to use 20 kilogrammes of TNT to blow up the railway line in the country's north linking Iran to Europe.
The authorities have regularly accused the United States and Britain of seeking to stir unrest amongst ethnic minorities in its sensitive border areas close to the Turkish, Iraqi and Pakistani frontiers.
The clashes in West Azarbaijan come almost two weeks after 13 members of the guards were killed when a car bomb ripped through a bus carrying them to a base in the southeastern border province of Sistan-Baluchestan.