Russian Federation and Iran renewed their support for the Syrian government in a flurry of calls on Sunday, saying last week's US missile strike violated Syrian sovereignty but failed to boost the morale of "terror groups" in Syria.
Video: What changed Trump's mind about Assad?
Haley said Syria needs a president who protects his people, and, "Assad is not that person".
In September, The U.N. Security Council ordered Syria to account for and destroy its chemical weapons stockpile, and threatened to authorize the use of force in the event of non-compliance.
"It just - if you look at his actions, if you look at the situation, it's going to be hard to see a government that's peaceful and stable with Assad".
While Nikki Haley, the US ambassador to the United Nations, described regime change in Syria as a USA priority and inevitable, Tillerson suggested that last week's American airstrikes in retaliation for the chemical attack hadn't really changed USA priorities toward ousting Assad.
So Trump's decision to launch the strikes - which President Barack Obama declined to do after a 2013 chemical attack - has raised optimism among rebels that Trump will more directly confront Assad.
On Thursday, Trump ordered the US military to strike an airbase in Syria with several dozen Tomahawk missiles. Few seemed shocked by the prospect that Assad's government had secretly held onto some of its stash.
Syria and its close ally Russian Federation say that Islamic State and al-Qaida-linked militants in Syria have acquired chemical weapons.
"We are prepared to do more", he said.
October 14, 2013: Syria becomes a signatory to the Chemical Weapons Convention, prohibiting it from producing, stockpiling or using chemical weapons.
Few Americans desire USA military involvement in Syria beyond airstrikes, however, with 18 percent supporting the use of ground troops.
Foreign ministers from the Group of Seven main industrialised countries are meeting in the Italian town of Lucca later on Monday before US Secretary of State Rex Tillerson flies to Moscow on Tuesday.
US goals in the region, McMaster said, are "the defeat of ISIS" and "a significant change in the nature of the Assad regime and its behavior in particular".
"Those who have taken over USA affairs once claimed they wanted to combat terrorism; however, today Syria's terrorists are happy about [the] US invasion in Syria and are celebrating it", he said.
"From now on we will respond with force to any aggressor or any breach of red lines from whoever it is and America knows our ability to respond well", read part of a statement Sunday from a so-called "shared operations room" believed to include Russia, Iran and militias backing Syrian President Bashar al-Assad's regime. "Those who think that by supporting terrorists, they can change Syria's future in their interest, are absolutely wrong", Rouhani said.