Mr. Rouhani made a phone call to President Bashar al-Assad following the U.S. missile attack on a Syrian airbase earlier last week.
Amid rising tensions between Moscow and Washington, Johnson said Saturday the situation in war-torn Syria had "fundamentally" changed following a chemical weapons attack on civilians and the USA airstrikes targeting a military airfield.
Both Tillerson and HR McMaster, Trump's national security adviser, said defeating the Islamic State group remained the administration's first priority, with the strategy for stabilizing Syria a longer-term political effort that could involve Russian Federation.
"What Ambassador Haley pointed out was, it's very hard to figure out how a political solution could result from the continuation of the Assad regime", McMaster said.
John McCain (R-AZ) said the administration of President Donald Trump was "probably was partially to blame", for the deadly chemical weapons attack in Syria. "And saying, 'we are only going after chemical weapons areas, ' ignores the enormity of the problem", he said.
McMaster, who has reportedly been gaining power in the Trump White House, said on Fox News that while the US backs regime change, it won't be the country who is "going to effect that change".
The US and United Kingdom are expected to tell Russian Federation it must stop supporting the regime of Syrian President Bashar al Assad and instead help with drawing up a plan to rebuild the country.
"This was something that needed to tell Assad, 'Enough is enough.' And this is something to let Russian Federation know, 'You know what?"
For the millions of Syrian refugees scattered across camps and illegal settlements across the region, the chemical attack on a town in northern Syria and subsequent US strike was a rare moment when the world briefly turned its attention to Syria, before turning away again.
He wrote: "By sending Tomahawk missiles to attack the airfield, aeroplanes and equipment believed to be involved, it has sent a strong signal to the Syrian regime to think twice before using gas in the future".
The United States has conducted air strikes against Islamic State, which controls territory in eastern and northern Syria, and a small number of US troops are helping rebel militias.
USA air strikes were criticised by Bashar al-Assad's allies. We know there's no easy solution to the crisis that's in Syria.
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".
Is political transition a reality in Syria?
U.S. Secretary of State Rex Tillerson denied in an interview on CBS's Face the Nation that the strikes signaled an overhaul of American policy, saying its priority remained to defeat Islamic State militants in the Middle East.
The gassing of civilians, including children, in the town of Khan Sheikhoun last week appears to have changed Mr. Trump's mind on Syria. "In fact, we were prepared to do more two days ago", McMaster said. A very small percentage of the people have been slaughtered in Syria have been slaughtered by chemical weapons.
"So, there's multiple priorities", she said.
Asked if Mr. Trump was considering slapping tougher sanctions on Russia, Ms. Haley said such moves are now under consideration.