The US is looking into whether the move violates UN resolution prohibiting supply, sale and transfer of combat aircraft to Iran
Russia launched a second day of air strikes against Syrian militants from an Iranian air base, rejecting US suggestions.
State Department spokesman Mark Toner on Tuesday called the Iranian deployment "unfortunate," saying the United States was
looking into whether the move violated UN Security Council resolution 2231, which prohibits the supply, sale and transfer of
combat aircraft to Iran.
Russia bristled at those comments on Wednesday after announcing that Russian SU-34 fighter bombers flying from Iran's Hamadan air base had for a second day struck Islamic State targets in Syria's Deir al-Zor province, destroying two command posts and killing more than 150 militants.
"It's not our practice to give advice to the leadership of the US State Department," Major-General Igor Konashenkov said in a statement.
"But it's hard to refrain from recommending individual State Department representatives check their own logic and knowledge of basic documents covering international law."
Moscow first used Iran as a base from which to launch air strikes in Syria on Tuesday, deepening its involvement in the five-year-old Syrian civil war and angering the United States.
Russia's use of the Iranian air base comes amid intense fighting for the Syrian city of Aleppo, where rebels are battling Syrian government forces backed by the Russian military, and as Moscow and Washington are working towards a deal on Syria that could see them cooperate more closely.
Russia backs Syrian President Bashar al-Assad, while the United States believes the Syrian leader must step down and is supporting rebel groups that are fighting to unseat him.
On Wednesday the State Department reiterated its concern, saying Russia's use of the Iranian base "doesn't help" reach a cessation of hostilities in Syria and that U.S. lawyers were still assessing whether it violated the UN resolution.
Russian Foreign Minister Sergei Lavrov said earlier any US dismay over Moscow's military co-operation with Iran should not distract from efforts to realise the U.S.-Russia deal on coordinating action in Syria and securing a ceasefire.
Lavrov said there were no grounds to suggest Russia's actions had violated the UN resolution, saying Moscow was not supplying Iran with military aircraft for its own internal use, something the document prohibits.
"These aircraft are being used by Russia's air force with Iran's agreement as a part of an anti-terrorist operation at the request of Syria's leadership," Lavrov told a Moscow news conference, after holding talks with Murray McCully, New Zealand's foreign minister.