The two men "condemned the American operation against a Syrian airbase which is an aggression against an independent country", Iran's state news agency IRNA said.
Moscow, Assad's key backer, has supported the Syrian government militarily in the ongoing conflict since 2015.
On Friday, the United States carried out missile strikes on a Syrian air base it says is suspected of storing chemical weapons.
Boris Johnson, the British foreign secretary, is pushing for the group, which comprises the United States, Canada, France, Germany, Italy, Japan and the United Kingdom, to call for Russian Federation to drop backing for the country's president Bashar al-Assad or face tough new sanctions, The Times reported.
McMaster told Fox News Sunday host Chris Wallace the "president acted decisively" and that while the strike wasn't meant to take out all of Syria's capabilities, "it was a strong signal that the USA will not stand idly by". "And I'm sure when they can declassify that, they will".
Lawmakers say President Donald Trump needs to work with Congress on a "long-term" Syria strategy following last week's US missile strike.
"President Bashar al-Assad should resign and leave power, for the love of Syria, allowing the dear people of Syria to avoid war and the scourge of terrorism", he said.
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"If this intervention is limited only to an air base, if it does not continue, and if we don't remove the regime from heading Syria, then this would remain a cosmetic intervention", he said. The United States and other Western countries have thrown their support behind rebels fighting the Syrian regime.
Iran and Russian Federation are Assad's closest allies and label all opponents of his regime as "terrorists".
Iran has provided crucial military and economic assistance to Assad throughout Syria's six-year civil war.
"I think the real failure here has been Russia's failure to live up to its commitments under the chemical weapons agreements that were entered into in 2013", Tillerson said on ABC's This Week.
The Russian Defense Ministry said on Wednesday that the airstrike near Khan Shaykhun by the Syrian air force hit a terrorist warehouse that stored chemical weapons slated for delivery to Iraq, and called on the UN Security Council to launch a proper investigation into the incident.
Sir Michael went on that there must now be a longer-term solution to the conflict that does not involve Mr Assad, adding: "Someone who uses barrel bombs and chemicals to kill his own people simply can not be the future leader of Syria".
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