The dispute is the latest between the two countries as they line up on different sides of the Syrian civil war. While they both oppose ISIS, which has used the chaos to establish a safe-haven there, the US wants to see close Russian ally Bashar al-Assad leave power while Russia continues to back the regime with airstrikes against Syrian opposition groups.
US State Department spokesman Mark Toner told reporters Tuesday that Russia's use of the Iranian airfield "could very well be a violation of Resolution 2231," which prohibits the transfer of combat aircraft to Iran.
But Russian Foreign Minister Sergey Lavrov denied that the Russian move breached the resolution.
"There are no reasons to suspect Russia of violating resolution 2231," Lavrov said during a news conference Wednesday. "Neither supply nor transfer or sale of military aircraft to Iran took place."
A Russian Defense Ministry spokesman took a more direct swing at the US.
"One should check the knowledge of the UN resolution," Maj. Gen. Igor Konashenkov said in a statement issued Wednesday in response to the State Department's comments.
Toner told reporters Wednesday that the actual language of the resolution is very nuanced.
"It has gradations, if you will, on what you can or cannot do with regard to providing or giving Iran offensive capabilities," he said.
The text prohibits the use of combat aircraft "for the use in or benefit of Iran." Because Iran supports the regime of Assad in Syria with proxy fighters and because Russian airstrikes there are in support of Assad's government, it is possible that the aircraft could be seen as being used for the "benefit of Iran."
"So we're looking at it and we're trying to make a sober assessment of whether this constitutes, in our view, a violation," Toner added.
State Department officials confirmed that the department's lawyers are examining the matter.
Anthony Cordesman of the Center for Strategic and International Studies called the housing of Russian bombers in Iran as representative of "a major strategic shift in the Middle East" that is likely to frustrate US efforts to contain Iran's influence in the region.
Cordesman assessed that the US would certainly consider steps like raising the issue with the UN in an attempt to push back against the emerging Iran-Russian collaboration.
Konashenkov, for his part, questioned the legality of the American campaign against ISIS in Syria.
"Is there any UN Charter provision, UN Security Council resolution or a bilateral treaty between the USA and Syria authorizing bombing of the Syrian territory by attack UAVs of the US Air Force?" Konashenkov asked.
Toner, however, defended the US campaign.
"We believe that we have the authorization, the legal authority rather, to use military force against ISIL in Iraq and in Syria," he told reporters, using a different name for ISIS.
The spat has raised questions about the prospect of proposed US-Russia cooperation
on fighting ISIS and Jabhat Fateh Al-Sham, formerly known al Qaeda's Syria affiliate, the Nusra front.
The two nations operate in close proximity, and the US expects the deal will include a grounding of Assad's air force in exchange for providing more information to the Russians about US missions.
Toner said Tuesday that Russia's actions did "not preclude the fact that we will reach some kind of cooperative arrangement with Russia. We continue to pursue that."
But when asked about such a collaboration by CNN's Clarissa Ward Wednesday, the former American ambassador to Syria, Robert Ford, said, "It's not at all clear you can trust the Russians."