"Someone who uses barrel bombs and chemicals to kill his own people simply can not be the future leader of Syria", he said.
Russian President Vladimir Putin and Iran's Hassan Rouhani said in a phone call that aggressive USA actions against Syria were not permissible and violated worldwide law, the Kremlin said.
"Regime change is something that we think is going to happen", Haley replied.
According to Idlib's opposition-run health authority, 89 people, including 33 children and 18 women, died in the suspected nerve agent attack in the rebel-held town of Khan Sheikhoun on Tuesday.
Days later, after a chemical weapons attack on Syrian civilians that the US blames on Assad's regime, the Trump administration sharpened its rhetoric and launched several dozen cruise missiles at a Syrian airfield, marking the first USA military effort against the Assad government.
Russian minister for foreign affairs Sergei Lavrov and USA secretary of state Rex Tillerson spoke by phone on Saturday about the situation in Syria after U.S. strikes on a Syrian air base, the Russian foreign ministry has said in a statement.
Moscow is responsible "by proxy" for the deaths of civilians as the "principle backer" of the Syrian government, Fallon told British Media.
McMaster's comment came ahead of a planned visit to Moscow by Secretary of State Rex Tillerson - a trip that has become exponentially more sensitive after Trump ordered missile strikes against a Syrian airfield on Thursday.More news: Dozens of kids participate in Easter egg hunt in Unicoi Co
The US will keep up pressure to remove Syrian dictator Bashar al-Assad.
"You need more American troops to accelerate (ISIS') demise", Graham told NBC's "Meet the Press".
Speaking two television programs Sunday, Tillerson said that he had not seen any conclusive evidence that Russians were involved in carrying out the chemical weapons attack.
"Tonight I call on all civilized nations to join us in seeking to end the slaughter and bloodshed in Syria and also to end terrorism of all kinds and all types".
Graham also argued Sunday that the United States is "relying too much" on the Kurds in that region to defeat ISIS and that additional USA troops would attract more regional fighters in that effort.
"I do not believe that the Russians want to have worsening relationships with the U.S., but it's going to take a lot of discussion and a lot of dialogue to better understand what is the relationship that Russia wishes to have with the United States".
Boris Johnson cancelled the visit, scheduled for 10 April, on Saturday, saying events in Syria had changed priorities.