Mr Corbyn described the Salisbury attack as an "appalling act of violence", as he urged the government to ensure its response is "decisive, proportionate and based on clear evidence".
He said the most likely explanation was Russian Federation that was "directly or indirectly responsible" for the attack but "culpability takes many forms".
"So, there is a history of problems in relation to interpreting that evidence but, in this case, the Government may well have other evidence that we are not aware of".
Speaking to reporters after the statement updating MPs on the poisoning in Salisbury, the spokesman indicated that Labour does not believe there is enough evidence yet to blame the Russian state for the attack.
Jeremy Corbyn has cast doubt on evidence that led the Government to blame Russian Federation for the Salisbury attack, pointing instead to the "WMD" saga before the Iraq War as reason to be suspicious of Theresa May's approach.
Russia, also a member of the Security Council, has denied any involvement in the attack.
Mr Woodcock said: "This is a time for the nation to speak as one so it was heartening that the overwhelming majority of MPs of all parties spoke so strongly in support of the strong package of measures outlined by the Prime Minister today".
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It does not address the topic of gun control . "Clearly, the NRA was more persuasive than I was". A mass shooting in Parkland , Florida last month has renewed a USA debate over gun control .
Labour's Yvette Cooper, chair of the Home Affairs Select Committee, was cheered by MPs on all sides of the chamber when she said Russia's actions should be met with "unequivocal condemnation".
And former Labour minister Pat McFadden said showing resolve when your country was threatened was an "essential component of political leadership" and "more than words" was needed as a response.
The motion was swiftly signed by a number of prominent critics of Mr Corbyn, some of whom went public with their criticism of the leader's senior aide Seumas Milne. After the Labour leader failed to say that he believed Russian Federation to be responsible for this attempted murder, his spokesman went one further in the post-PMQs briefing.
"There should be no doubt over Russia's culpability and we should resist the Russian propaganda machine's attempts to sow the seeds of doubt in the minds of the British people". In fact, so were the SNP and the Liberal Democrats - it was really just Corbyn who was the odd one out.
Mr Corbyn was then barracked from the Conservative benches for using the exchanges - in which MPs largely supported Mrs May's response to what she branded an "unlawful use of force by the Russian state against the UK" - to suggest the UK's diplomatic capacity has been reduced as a result of cuts.
Russian Foreign Minister Sergei Lavrov has said the United Kingdom is bound to provide a sample of the nerve agent used in the attack to Russian investigators under worldwide treaties, something Ms May has withheld.
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