At a meeting of the three countries' foreign ministers in Moscow on Friday, Russia’s Sergey Lavrov denounced the US attack on a Syrian military airfield earlier this month, calling it a "flagrant violation" of international law.
Lavrov said Washington was seeking "excuses for regime change" in Syria.
"These attempts will not succeed, this will not happen," he said.
Washington launched 59 missiles at the Syrian airbase after a chemical attack in Idlib province on 6 April that Western powers blame on the Syrian government. US officials have threatened additional strikes if chemical weapons are used again.
Russia, Iran and Syria have rejected the West's accusations.
Syrian Foreign Minister Walid Moallem said the three countries have "common procedures against any aggression", adding that the meeting in Moscow sends a message to the United States.
Russia on Wednesday vetoed a UN Security Council resolution to condemn the chemical attack and demand the Syrian government’s cooperation with an international investigation into the incident.
Mohammad Javad Zarif, Iran’s top diplomat, stressed that Tehran, Moscow and Damascus object to unilateral US actions.