Mr Tillerson said he did not know whether the Russian government had knowledge of the poisoning, which left former Russian double agent Sergei Skripal and his daughter Yulia in critical condition earlier this month.
But he said the poison used is known to the US, and does not exist anywhere outside Russia. The substance, he added, is “only in the hands of a very, very limited number of parties”.
“Those responsible – both those who committed the crime and those who ordered it – must face appropriately serious consequences,” said Mr Tillerson, who spoke by phone with British Foreign Secretary Boris Johnson on Monday.
He did not specify what these consequences would be.
The comments echo those of British Prime Minister Theresa May, who said it was “highly likely” Russia carried out the attack. Ms May identified the poison as Novichok, a military grade nerve agent developed in the Soviet Union in the 1970s.
“We shall not tolerate such a brazen act to murder innocent civilians on our soil,” the prime minister said.
Russia has denied any involvement in the attack, and called Ms May’s comments “a circus show”.
Mr Tillerson’s comments marked an escalation in the US’s response to the attack. Press Secretary Sarah Huckabee Sanders had previously called the episode “reckless, indiscriminate and irresponsible,” but refused to blame Russia.
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Mr Skripal previously worked with Russia’s military intelligence unit, and then with the country’s Foreign Ministry. He was arrested in Moscow in 2004 and confessed to having been recruited by British intelligence almost 10 years earlier. He was sentenced to 13 years in prison in 2006, but was later pardoned as part of a US-Russia spy swap.
Mr Skipal’s 33-year-old daughter was thought to be one of his only living relatives, after his wife and son died.
The attack took place in Salisbury, some 90m (154km) from London. Mr Skipal and his daughter were later found unconscious on a park bench. Almost two dozen people have already received medical treatment in connection with the attack, which authorities say may have contaminated up to 500.
Ms May has given Russian President Vladimir Putin 24 hours to explain how the Russian position was used in the attack, threatening “extensive measures” if he did not come up with a credible explanation.
Additional reporting by agencies