Writing for The Independent, the senior Labour figure issued a plea not to brand as “disloyal” those who – like himself – have defied the party leader to call for a ceasefire in Gaza.
Mr Burnham also urged that lessons are learned from the flawed response to 9/11 terror attacks – arguing that Israel’s actions against Hamas “should be as targeted as possible”.
At least 13 Labour frontbenchers are opposed to Sir Keir’s position, with a host of shadow ministers and devolved leaders breaking ranks in recent days.
Mr Burnham said it was “healthy” for the party to share different views and that the current crisis was “an entirely different situation” to normal politics in a plea for understanding.
“In times like this, it is simply not possible quickly to arrive at a clear party line,” said the influential Manchester mayor. “People will have different views and it is healthy for those views to be aired.”
Mr Burnham added: “MPs’ feelings will change daily as they react to events, balance views of constituents and try to formulate a settled view. Let’s not brand them as disloyal or as if they don’t care about innocent lives.”
Sir Keir will not sack shadow ministers rebelling over the party’s refusal to back a ceasefire in Gaza, frontbencher Peter Kyle indicated on Sunday.
The shadow science secretary told the BBC that the Labour leadership would “continue engaging” with the dozen or so frontbenchers unhappy with Sir Keir’s stance.
However, Left-wing Labour MP Andy McDonald has had the party whip suspended after using the phrase “between the river and the sea” at a rally this weekend.
Some pro-Palestinian protesters have chanted “from the river to the sea, Palestine will be free” during recent demonstrations in London, despite controversy around the slogan’s meaning.
A Labour spokesperson said: “The comments made by Andy McDonald at the weekend were deeply offensive, particularly at a time of rising antisemitism which has left Jewish people fearful for their safety. The chief whip has suspended the Labour whip from Andy McDonald, pending an investigation.”
Sir Keir has called for a “humanitarian pause” in the fighting to allow for aid to be delivered to civilians – but continues to support Israel’s right to defend itself as it steps up its ground invasion.
Mr Burnham urged support for Sir Keir, his shadow cabinet and all Labour MPs – arguing that they should have “the support and space they need to face the defining challenge of our generation”.
But the Greater Manchester mayor issued a warning about the lessons that should be learned from the US-UK invasion of Iraq after 9/11.
“While there remains a case for the removal of Saddam Hussein, I can’t justify the rage, the rhetoric, the haste with which it was done nor the lack of a plan for the aftermath,” Mr Burnham wrote. “If the response to 9/11 was supposed to root out terrorism, it is hard not to conclude it did anything but,” he added.
Despite Mr Burnham’s call for a ceasefire, the Labour mayor said he supports “any nation’s right to respond to terrorism to protect their citizens, including Israel’s [right]”.
“If the goal is to end terrorism, my experience tells me that action should be as targeted as possible and avoid any sense that it is disproportionate or indiscriminate,” he wrote.
“It should not be taken in haste but with a clear, understood plan for the aftermath. Wherever possible, politicians should create space for people on both sides to come together and lead the response.”
Former Gordon Brown adviser Ian Austin – a former government adviser on antisemitism – said Mr Burnham’s remarks showed “breath-taking narcissism and self-indulgence, even by his Olympic-level, nuclear-powered, ocean-going standards”.
And the Jewish Representative Council (JRC) of Manchester has written to Mr Burnham to say the ceasefire call shows “a lack of understanding to the challenges currently being encountered by Israel”.
Shadow ministers Naz Shah, Paul Barker and Afzal Khan have all openly challenged Sir Keir’s refusal to support a ceasefire, after Scottish Labour leader Mr Sarwar and mayors Mr Khan and Mr Burnham all defied the leadership.
Shadow veterans minister Rachel Hopkins, shadow local government minister Sarah Owen, shadow domestic violence minister Jess Phillips, and Labour whip Kim Leadbeater all retweeted calls for a ceasefire on Twitter/X at the weekend.
Labour’s shadow justice secretary Shabana Mahmood has also appeared to drift from the “party line” by warning Israel against any “collective punishment” of civilians in Gaza.
The Labour leader has also angered many in the party with comments on LBC Radio in which he appeared to back the cutting of power and water to Gaza – which he clarified 10 days later, insisting: “I was not saying that Israel had the right to cut off water, food, fuel or medicines.”