He said those responsible for the attack on Mr Skripal and his daughter Yulia in Salisbury “must face serious consequences”.
“There is never a justification for this type of attack, the attempted murder of a private citizen on the soil of a sovereign nation, and we are outraged that Russia appears to have again engaged in such behavior,” said Mr Tillerson.
The secretary of state’s remarks came hours after the White House publicly condemned the poisoning in the UK but refused to link it to Russia.
On Monday afternoon, Theresa May told the House of Commons that the nerve agent used in the attack was “of a type developed by Russia”.
“Either this was a direct action by the Russian state against our country or the Russian government lost control of the agent and allowed it to get into the hands of others,” she said.
Mr Tillerson said in a statement: "We have full confidence in the UK's investigation and its assessment that Russia was likely responsible for the nerve agent attack that took place in Salisbury last week.
"There is never a justification for this type of attack - the attempted murder of a private citizen on the soil of a sovereign nation - and we are outraged that Russia appears to have again engaged in such behaviour.
"From Ukraine to Syria - and now the UK - Russia continues to be an irresponsible force of instability in the world, acting with open disregard for the sovereignty of other states and the life of their citizens.
"We agree that those responsible - both those who committed the crime and those who ordered it - must face appropriately serious consequences.
"We stand in solidarity with our allies in the United Kingdom and will continue to coordinate closely our responses."
Sergei and Yulia Skripal were left in critical conditions following the poisoning in Salisbury town centre, while the first police officer on the scene also became seriously ill.
The Russian government continued to deny any involvement in the attack in a statement released earlier on Monday.
A statement from the Russian Embassy reads: "The investigation is being concluded in a non-transparent manner, whenever for the Russian side nor for the public. Quite naturally, this is a source of concern.
"We would like to stress once again that we are outraged by the anti-Russian media campaign, condoned by the Government, that influences the investigation and has a psychological effect on British residents.
"Current policy of the UK Government towards Russia is a very dangerous game played with the British public opinion, which not only sends the investigation upon an unhelpful political track but also bears the risk of more serious long-term consequences for our relations."
Home Secretary Amber Rudd will chair a meeting of the Government's Cobra emergencies committee in Whitehall at 11.30am on Tuesday to assess the latest position.