While the Labour leader has refused to condemn the Kremlin, his right-hand man Mr McDonnell is the latest to back the Prime Minister.
He said the poisoning is “highly likely” to have been a state execution despite Mr Corbyn wanting more evidence.
Mr McDonnell told ITV’s Peston on Sunday: “He [Putin] is responsible whichever way you look at it, all the evidence points to him.”
He added: “We support exactly what the Prime Minister said and we condemn Russia for this. This is a pattern of behaviour we have seen.”
Mr McDonnell said we must base judgments on evidence but added: “There’s a pattern of people being murdered here, leading you to the conclusion that Putin has questions to answer because this is highly likely to have been a state execution.”
Mr Corbyn’s chief adviser Seumas Milne named MI5 as the culprits but 30 Labour MPs have signed an early day motion supporting Mrs May.