The strikes came after a chemical attack killed 89 people in the opposition-held Idlib Governorate.
"The current state of U.S. Russian Relations is at a low point", Tillerson, who is in Moscow for meetings, said at a joint news conference Wednesday.
The toxic gas attack on April 4 prompted the U.S. to launch missile strikes on a Syrian air base and widened a rift between USA and Russian relations. "I would like to think that they didn't know, but certainly they could have", Trump said.
Not long before Trump spoke, Russian Federation vetoed a Western-backed United Nations resolution that would have condemned the chemical weapons attack and demanded a speedy investigation.
Despite the tensions between the two countries, both Russian Federation and the USA agreed to fight worldwide terrorism and continue discussions on Syrian conflict settlement.
US President Donald Trump said that US's ties with Russian Federation may be at "an all-time low".
The shape of these relations will also greatly influence the region, which watches with interest the spar between the two giants pumped up by too much ego and with too many interests vested to make them pliant.
Mr Tillerson said there was no doubt that the attack had been planned and executed by the Syrian regime, which has used chlorine bombs on more than 50 occasions.
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Syrian President Bashar al-Assad said an alleged poison gas attack blamed on his government last week in Idlib province was "100 percent fabrication" used to justify a USA air strike, news agency AFP reported on Thursday.
His comments came after US President Donald Trump said Mr Putin was backing an "evil person" in Assad, as talks took place in Russian Federation between the countries' chief diplomats.
He reiterated the United States position that Assad must eventually relinquish power in Syria.
Lavrov told reporters there are issues to be overcome.
He also rejected American claims of certain evidence that Assad ordered the chemical attack.
"I would like to commend the position of the Russian government, Russian President Vladimir Putin and the Russian people concerning the USA aggression", Muallem said.
The US president appeared to indicate on Tuesday that he had no intention of having US armed forces bogged down in Syria and would concentrate on defeating the Isis death cult rather than overthrowing President Bashar al-Assad. The California Republican told CNN's Wolf Blitzer this week that he believes authorization would be necessary only if the Trump administration takes military action against Assad for a duration longer than 60 days, the amount of time the executive branch is provided to take military actions without congressional approval in the War Powers Act.
"It's deplorable, and we regret what is going on, but we can do little except asking to back accusations with facts", Lavrov said.