"When relations are at the lowest point, there's nowhere to go but up," McMaster told ABC News.
His comments came at a time when US President Donald Trump has abandoned his soft line on Russia in recent weeks and said US relations with Russia "may be at an all-time low."
Soon after his coming into office on January 20, Trump, who praised Russian President Vladimir Putin throughout his election campaign, had appeared to go ahead for a potentially historic rapprochement with Russia.
"Russia has given support to a murderous regime in Syria, that has perpetuated a civil war and as cycle of violence that, along with obviously the brutal... Actions of ISIS, has brought suffering to so many people, has created a crisis within Syria that has bled over into Iraq, has bled over into neighbouring countries and into Europe and so forth," he said.
Trump last week ordered air strikes on a Syrian air base in retaliation for a chemical weapons attack in which more than 80 people died. The US has described the use of chemical agent as a nerve gas attack that Syrian President Bashar al- Assad ordered.
Assad denied and Russia said rebels were responsible for the attack.
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