At a lecture in central London last night Thornberry said: "You don't have to be a lawyer, like so many in this room, to know that when there is prima facie evidence against a suspect, then that suspect has a case to answer".
The attack in Salisbury was an appalling act of violence, which we condemn in the strongest terms.
Ms Griffith told the BBC the party accepted "Russia was responsible".
Corbyn had called for any action to be "decisive and proportionate, and based on clear evidence".
Meanwhile, fellow Labour backbencher John Woodcock - a regular critic of Mr Corbyn - revealed he is gathering signatures for a parliamentary motion among Labour MPs, to make it clear they "unequivocally accept Russia's culpabililty in the Salisbury attack" and support the Government's actions.
Speaking on BBC Radio 4's Today programme, Ms Griffith said: "We very much accept that what the prime minister said - this is a very sophisticated nerve agent and Russian Federation is responsible for this attack and therefore we're fully supporting the measures which the government is taking, including the expulsion of 23 diplomats".
The Labour leader was responding to the Prime Minister's statement in which she announced a series of measures against Russian Federation after it failed to meet her midnight deadline to explain the attack.
When pressed on the issue and his shadow defence secretary's comments, Corbyn said: "The evidence points towards Russian Federation on this, therefore responsibility must be borne by those that made the weapon, those that brought the weapon into the country and those that used the weapon".
"In the meantime I think it is essential we follow the evidence and what the evidence produces", he added.
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He also avoids criticizing Trump. "It could happen, it doesn't happen", Trump said of the meeting. TRUMP: They're saying Obama, Obama, Obama. "Time and place to be determined".
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Several shadow ministers are known to have been angered by their leaders' tone, triggering speculation that Mr Corbyn could face resignations from his top team.
Speaking in the Commons, Mr Corbyn condemned the "appalling" attack but pressed Theresa May on whether the United Kingdom had supplied traces of the nerve agent used in the attack to Russian Federation for analysis before Wednesday's deadline, as the Kremlin had asked.
He added: "The evidence points towards Russian Federation on this, therefore the responsibility must be borne by those that made the weapon, those that brought the weapon into the country and those that used the weapon".
'What I was asking was questions, questions about the identity of the weapon, questions about the reference to the weapons convention and also the support of other allies.
She also distanced herself from Corbyn's spokesman, saying she "can't speak for Seumas Milne", and that he "has to speak for himself".
Speaking to journalists after PMQs, Milne said: "The prime minister said that there were two possibilities - either the Russian state was directly responsible for the attack or it had negligently allowed weapons-grade nerve agent to fall into the hands of others".
But the spokesman said such moves risk starting a "tit for tat" response and that measures to "hit them in the pocket" would be more effective. However, also there is a history in relation to weapons of mass destruction and intelligence which is problematic, to put it mildly.
There is a clear divide between Jeremy Corbyn's office and those in the party who struggle with his position on national security and foreign policy.