Assad's 'murderous rampage' must be stopped: McCain

US Senator John McCain, an advocate for a tougher stance on Syria for years, demanded the end of Damascus' "murderous rampage" on Tuesday, saying Moscow should cease its support for the regime.

Syrian President "Bashar al-Assad must be stopped in this murderous rampage that continues," McCain told reporters in Sarajevo during a tour of the Western Balkans.

"I was glad to see our Secretary of State just today say the Russians should divorce themselves from the conduct of Bashar al-Assad," the Republican said.

McCain hailed as a "credible first step" the US air raids on Syria last week in response to an alleged chemical attack that Washington has blamed on Assad's regime.

The senator urged a new strategy aimed at putting Assad's air forces out of combat.

"I believe we should not have Bashar al-Assad's air force continue the indiscriminate murdering of innocent civilians," McCain said, calling the Syrian president a "war criminal" and urging his defeat along with the Islamic State group.

"When some of our leaders say, 'Well first we have to take care of ISIS then take care of Bashar al-Assad' - the US are the most powerful nation on earth, we can do both at same time," he said, using an alternative acronym for the militant group.

He also lashed out at Russian military operations in Syria, saying that to a mother who loses her child as a result of actions by the regime or its ally, it "really doesn't matter much whether the child was killed by a chemical weapon or barrel bomb".

"Needless and senseless slaughter of innocent men, women and children is an obligation for all of us to stop, including Russians who use precision weapons to attack hospitals in Aleppo," McCain suggested.

Syria's war has killed more than 320,000 people since it started in 2011 with the brutal repression of anti-government protests.