They condemned the "first offensive use of a nerve agent in Europe since the Second World War", calling it an assault on UK sovereignty, BBC reported.
The UK has expelled 23 Russian diplomats in the wake of the incident.
British PM Theresa May on Thursday visited the site of the attack in Wiltshire.
"We do hold Russia culpable for this brazen, brazen act and despicable act," she said.
Russia has denied any involvement in the attack. It has vowed a swift response to the expulsion of its diplomats.
The statement says: "It is an assault on UK sovereignty and any such use by a State party is a clear violation of the Chemical Weapons Convention and a breach of international law. It threatens the security of us all."
The nations urged Russia to "address all questions related to the attack" and provide all details about the nerve agent used.
It added: "Our concerns are also heightened against the background of a pattern of earlier irresponsible Russian behaviour.
"We call on Russia to live up to its responsibilities as a member of the UN Security Council to uphold international peace and security."
Russia says it had nothing to do with the attack and will respond to UK measures against it.
The Russian embassy said the decision to expel its diplomats was "unacceptable, unjustified and short-sighted".
The embassy has also suggested on its Twitter feed that the UK may have the capacity to manufacture the nerve agent used in Salisbury.
It said Russia closed all Soviet-era chemical weapons programmes in 1992 and some of the scientists involved were flown to other countries, including the UK.
"To identify a substance, formula and samples are needed - means UK has capacity to produce suspected nerve agent," it said.