U.S. Secretary of State Rex Tillerson meanwhile plans to meet with G-7 foreign ministers in Europe next week before going on to Moscow.
On April 8, Iranian President Hassan Rohani called for an impartial probe into the alleged chemical attack in Syria.
In other developments, a Lebanese official close to the Syrian government said almost 12,000 people will be moved around Syria Wednesday in a planned population transfer arranged between the regime and rebels.
Iranian President Hassan Rouhani said on Saturday that "terrorists" were applauding his United States counterpart Donald Trump for launching a missile strike on an airbase of his Syrian government ally. "So, yes, I'm skeptical", she said.
The US strike Thursday was created to be a targeted mission on the airfield from where the deadly chemical attack was launched Tuesday. But a spokesman for Russian President Vladimir Putin warned that the strikes dealt "a significant blow" to relations between Moscow and Washington.
Saudi Arabia, one of the most vehement opponents of Assad, said the missile barrage was the right response to "the crimes of this regime to its people in light of the failure of the worldwide community to stop it". He said his priority was to hold talks with Western allies about Syria and Russia's support for Assad. Earlier, U.S. military officials had said they were looking into whether Russian Federation participated, possibly by using a drone to help eliminate evidence afterward. Assad accused the US of trying to boost the morale of "terror groups" in Syria.
Trump's decision to strike Syria won widespread praise from other nations.
General Valery Gerasimov and Major General Mohammad Bagheri spoke by phone and "condemned the American operation against a Syrian airbase which is an aggression against an independent country", Iran's state news agency IRNA said.
But he suggested that Trump was seeking a global political response for regime change from US allies as well as Russian Federation, which he said needed to re-evaluate its support of Syria.
"What the Americans did is a strategic mistake and offense".
Trump's missile strike moves USA policy beyond containment and it will complicate the war against IS, but it remains a largely symbolic gesture at this stage. The Kremlin blamed the chemical weapons attack on terrorists, not on Assad's regime.
British Foreign Secretary Boris Johnson has canceled a planned trip to Russia because of fast-changing developments in Syria - prompting a mocking tweet and a Russian official to take a dig at the West.
"Do they want it to be a relationship of competition and potential conflict?" he continued.
Information for this article was contributed by Hope Yen, Josh Lederman, Philip Issa, Zeynep Bilginsoy, Jim Heintz and Nasser Karimi of The Associated Press; by Todd Shields and Ros Krasny of Bloomberg News; and by David E. Sanger of The New York Times.