Tensions within the Labour party have burst into the open after a succession of MPs, including two frontbenchers, openly challenged the authority of Jeremy Corbyn in the House of Commons over his response to the Islamic State threat.

In a sign of deteriorating relations in the party, a former parliamentary aide to Alistair Darling was told by the Corbyn-supporting grassroots Momentum group to “get behind the leader or kindly go” after she challenged Corbyn at a party meeting on Monday.

“I await the assassins to come out of the shadows,” Ann Coffey tweeted after the Momentum branch in her Stockport constituency issued the warning. The group subsequently deleted the tweet which had told Coffey: “You continue to disappoint and let down the people of #Stockport. Get behind the leader or kindly go.”

Momentum turned on Coffey after she joined forces with other MPs to challenge Corbyn at a meeting of the parliamentary Labour party. Corbyn faced pointed questions over his claim that Britain’s involvement in the Iraq and Afghan conflicts helped to explain the rise of Isis and his comments in a BBC interview that he was not happy with a policy of shoot-to-kill against terrorists on British streets.

In his leader’s report to Labour’s national executive on Tuesday, Corbyn clarified his remarks as he said he would authorise the use of lethal force against terrorists in British in exceptional circumstances to protect life if he was elected prime minister. “Of course I support the use of whatever proportionate and strictly necessary force is required to save life in response to attacks of the kind we saw in Paris,” Corbyn said.

Separately, Labour confirmed that Ken Livingstone, the former London mayor who is a veteran campaigner against the Iraq war and nuclear weapons, would co-convene a policy commission on defence for Labour with the shadow defence secretary, Maria Eagle. This is the commission that oversees the review of Trident, led by Eagle, who has expressed views in favour of renewing the nuclear deterrent.

Labour sources said Corbyn’s remarks were designed to show that he would abide strictly by the law in authorising the use of force against terrorists. In the first place, “proportionate” force covers circumstances where non-lethal force is appropriate. In the second place, “strictly necessary force” covers circumstances such as the Bataclan shootings in Paris on Friday, where lethal measures by security forces are required to protect life. Corbyn would authorise this force in such circumstances.

The Labour leader clarified his thinking after eight Labour MPs, including two frontbenchers, signalled their concerns about Corbyn’s remarks on the use of lethal force by the security forces and the reasons behind the rise of Isis.

Pat McFadden, the shadow Europe minister, highlighted a speech Corbyn had intended to deliver last Saturday to Labour’s east of England conference. Corbyn, who cancelled his speech after the Paris attacks, had been due to say that Britain’s involvement in “a succession of disastrous wars increased, not diminished, the threats to our own national security”.

In remarks to David Cameron in the Commons on Tuesday, McFadden asked: “May I ask the prime minister to reject the view that sees terrorist acts as always being a response or a reaction to what we in the west do? Does he agree that such an approach risks infantilising the terrorists and treating them like children, when the truth is that they are adults who are entirely responsible for what they do?”

Cameron, who had given his statement on the Paris attacks and the G20 summit to the house, said to McFadden: “It is that sort of moral and intellectual clarity that is necessary in dealing with terrorists.”

Coffey had made a similar point at the parliamentary Labour party meeting on Monday when she said it was wrong to link the Iraq war with the shootings in Paris. In the Commons the MP for Stockport highlighted her unease with Corbyn when she told Cameron that Britain’s multiculturalism could be destroyed unless “every possible action” is taken to “defeat these murderous terrorists”.

David Hanson, the shadow foreign office minister, praised Cameron for setting out “with absolute clarity” that the government’s first duty is to protect its citizens. Chris Leslie, the former shadow chancellor, said: “Shouldn’t it be immediately obvious to everyone – to everyone – that the police need the full and necessary powers, including the proportionate use of lethal force if needs be, to keep our communities safe?”

Corbyn’s critics said the Labour leader’s equivocal approach on national security was a defining moment in his leadership. “I feel the Labour party is like a great ship of state holed below the waterline and is now gently sinking below the waves,” one former shadow cabinet minister said.

Labour sources said the criticisms were voiced by a vocal minority who had misrepresented Corbyn’s position on the use of lethal force. Corbyn had also made clear in the Commons that he was not isolated in his belief that the Iraq and Afghan conflicts contributed to the rise of Isis – Barack Obama said Isis was one of the “unintended consequences” of the Iraq war.