"Regime change is something that we think is going to happen because all of the parties are going to see that Assad is not the leader that needs to be taking place for Syria", Haley told CNN's 'State of the Union".
Washington blamed the Syrian government for the incident, saying chemical weapons used in the alleged attack originated from the airfield.
"The nation of Iran will remain alongside the Syrian nation in fighting terrorism and safeguarding Syria's territorial integrity", Rouhani said in the call on Saturday evening, according to a statement on the presidency website.
In an uncompromising article published today, Sir Michael Fallon warned that Moscow must bring Syrian President Bashar Al-Assad "to heel" in order to stop further atrocities in the war-torn Middle Eastern country.
Her comments appeared at odds with those of Secretary of State Rex Tillerson, who said the USA missile strike was aimed exclusively at deterring the use of chemical weapons by Assad.
"I think what we should do is ask Russian Federation how could it be, if you have advisors at that airfield, that you didn't know that the Syrian Air Force was preparing and executing a mass murder attack with chemical weapons?"
"I think it probably was partially to blame ..."
Damascus and Moscow denied Syrian forces were behind the gas attack but Western countries dismissed their explanation that chemicals leaked from a rebel weapons depot after an air strike.
McCain - who vocally supported the USA military response to the attack - added that the White House must put forward a detailed Syria strategy.
The Foreign Secretary said: "Crucially - they could do so again. Why are we supporting this murderous regime that is committing mass murder of its own population and using the most heinous weapons available?'"
Alex Salmond, the SNP's foreign affairs spokesman, said Mr Johnson looked "daft" for pulling out of a meeting with the Russians in Moscow. Reluctant to put significant troops on the ground in Syria, the USA for years has struggled to prevent Assad from strengthening his hold on power.
But he also clarified there had been "no change to our military posture" in Syria following a retaliatory USA strike against a Syrian airbase, and that Washington's "first priority" in Syria was to defeat the Islamic State terror group.
He called on Russian Federation to do "everything possible to bring about a political settlement in Syria and work with the rest of the global community to ensure that the shocking events of the last week are never repeated".
Johnson scrapped the trip just hours before he was due to fly out, saying: "We deplore Russia's continued defence of the Assad regime". "What America waged in an aggression on Syria is a crossing of red lines".
The centre also said the presence of USA troops in northern Syria, where it has hundreds of special forces helping the Syrian Democratic Forces to oust Isil, was "illegal".