The US has accused Iran of seeking to acquire nuclear arms and undermining security in the Middle East.
The UN has banned sensitive nuclear trade with Iran but there are no sanctions on conventional weapon deals.
"We don't think that it's an appropriate signal to be sending to the government of Tehran when they continue to be in defiance of UN Security Council resolutions," Tom Casey, a state department spokesman, said.
"We also believe as well that we certainly don't want to see any kind of lethal aid or assistance given to any country that's a state sponsor of terror. And as we've said, Iran is the leading state sponsor in the world."
Ivanov, also Russia's deputy prime minister, did not say how many missile systems had been delivered or when the deliveries took place.
Last year Russia dropped its plans to sell longer-range S300 anti-aircraft missiles to Iran, Russian news agencies reported.
The US at that time imposed sanctions on leading Russian arms firms over arms sales to Iran and Syria.