Labour legislator Chris Williamson, a Corbyn ally, called the critics "irrelevant malcontents" who were trying to undermine the party leader.
The latest criticism comes after Mr Corbyn accused the Prime Minister of "rushing way ahead of the evidence" for pointing the finger at Russian Federation over the Salisbury nerve agent attack.
Speaking to BBC Radio 4 Today programme, Ms Griffith said sought to realign Labour's position with the Government's, saying: "We very much accept that what the Prime Minister said, that this was a very sophisticated agent and that Russian Federation is responsible for this attack, and therefore we are fully supporting the measures which the Government is taking including the expulsion of the 23 diplomats".
Leaders from France, Germany, the USA, and United Kingdom also issued a joint statement on the attack, calling it the "first offensive use of a nerve agent in Europe since the Second World War".
Theresa May condemned the comments as "shocking" and "outrageous" after a Conservative MP raised them in the Commons chamber. "That very strongly is our front bench position".
Mrs May has blamed the Russian state for the attack with a Soviet-developed nerve agent that left Mr Sergei Skripal and his daughter in a critical state in hospital.
"What he needs to be more focused on is the fact that Russian Federation have a significant case to answer and our security services' advice to ministers and to the National Security Council can not be ignored or equated with weapons of mass destruction advice in a previous era". "Clearly this issue has to be followed on the basis of the evidence".
Splits have emerged between Mr Corbyn and key members of his shadow cabinet who have unequivocably backed Theresa May's handling of the Salisbury poisoning crisis.
It said: "The leader of the opposition's response to the prime minister was dispiriting".
Labour leader Jeremy Corbyn is in Cumbria.
We must not lose sight of the fact that is the first time a nerve agent has been used offensively like this on European soil since the Second World War.
It added: "Mr Corbyn's reluctance to share Mrs May's basic analysis of the Salisbury incident made him look eager to exonerate a hostile power".
'This has to be a time where we stand together with the Government, shoulder to shoulder, and with our North Atlantic Treaty Organisation allies, sending a very clear message to Russia, ' Mr Kinnock told BBC Radio 4's Today programme.
Mr Corbyn said that Mrs May was right on Monday to identify two possibilities for the source of the nerve agent - either Russian Federation authorised the attack or had lost control of the Novichok substance.
Asked if he could rule out the possibility of Russian Federation being framed, the spokesman said the evidence pointed "overwhelmingly" to the two options set out by the PM.
There are many Labour MPs who oppose Corbyn's left-wing views, but there has been a truce since he led the party to a better than expected result in last year's election.
Labour former minister Pat McFadden earlier told the Chamber: "Responding with strength and resolve when your country is under threat is an essential component of political leadership".
Ms Griffith's comments were quickly supported by several Labour MPs.
Nineteen Labour backbenchers have signed an early day motion, putting on the record their full backing for the prime minister and the measures she announced against Russian Federation, after some felt Corbyn's response to her statement on Wednesday was lacklustre.
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