Her comments come as reports suggest as many as 17 Labour frontbenchers expect to be sacked tomorrow for backing the SNP’s amendment to the King’s Speech.
All have put out statements or written or shared posts on social media also calling for an immediate end to the conflict.
Sir Keir Starmer’s position mirrors the government’s call for “humanitarian pauses” in the fighting.
That has put him at odds with Anas Sarwar, the Scottish Labour leader, who last month released a video calling for “a ceasefire right now.”
“That’s the only way we can see a safe, secure and free Palestine and a safe, secure and free Israel,” he said.
In an interview with the BBC’s Good Morning Scotland, Dame Jackie was asked if her party’s two Scottish MPs — Michael Shanks and Ian Murray — would be backing Mr Sarwar’s position or Sir Keir’s.
“Well, our position in Scotland has been very clear, Anas Sarwar backs a ceasefire, but the focus should be on what will help the people in Palestine and Israel just now,” she said.
The MSP added: “I think the situation is much too important for the kind of Punch and Judy politics we’ve been seeing.
“There’s not a hierarchy on whose lives are more important. I don’t want to see any more Israelis killed.
“I don’t want to see any more Palestinians killed. I absolutely want the fighting to stop. But we shouldn’t be game playing about this. We should be focused on what the solutions are.”
Dame Jackie said any ceasefire would need to be conditional on Hamas releasing all hostages.
“I talk about whether it’s a humanitarian pause or a ceasefire. For me in practical terms, it means the same thing.”
She added: “I would like to see, as my leader Anas Sarwar has said, we want to see a ceasefire. We want to see humanitarian pauses.
“You cannot watch premature babies dying in hospitals, because there’s no electricity to power incubators, and then start the kind of game playing that the SNP are engaged in.
“This is far too serious. We need serious heads considering how we stop the conflict and how we find the lasting solution for Israel and Palestine.”
The SNP amendment — which is likely, though not guaranteed, to be selected by the Speaker — will ask MPs to vote for the government to “join with the international community in urgently pressing all parties to agree to an immediate ceasefire”.
According to reports, calls for a ceasefire dominated a meeting of Labour’s parliamentary party (PLP) on Monday.
One MP told the Guardian: “Everyone is begging [Sir Keir] to do it,” they said after the highly charged meeting late on Monday night, where the shadow foreign secretary, David Lammy, attempted to hold the party line.
Pressed on whether Labour MPs would be allowed a free vote, the shadow chancellor, Rachel Reeves, told the BBC’s Today programme that this would be addressed when the party knew what amendments had been selected by the Speaker.
“There [are] a number of amendments down at the moment we don’t know what the vote will be on,” she said.
Pressed on what would need to happen in terms of the death toll before Labour backed a ceasefire, she said: “The numbers are already too high. Far too many innocent people in Israel and Gaza have lost their lives.”
“The way to stop this killing and the way to save lives is for the international community to come together and put pressure both on Hamas to release the hostages.”
The row comes as Mish Rahman, a member of Labour’s national executive committee from the West Midlands launches a grassroots campaign to put pressure on the leadership to back a ceasefire.
The SNP’s Foreign Affairs spokesperson Brendan O’Hara, said: “SNP MPs will be voting for an immediate ceasefire in Gaza and Israel.
“Parliament exists to consider matters of importance and the significance of this vote could be huge.
“We urge MPs of all parties to join the growing international momentum for a ceasefire to protect the lives of innocent children, prevent collective punishment and uphold international law.“
Meanwhile, Israeli ground forces continue to battle Palestinian militants around hospitals where patients, newborn babies and medics are stranded with no electricity and dwindling supplies.
The UN humanitarian office, known as Ocha, said only one hospital in the north is now capable of receiving patients.
All the others are no longer able to function and mostly serve as shelters from the fighting, including Gaza’s largest, Shifa, which is surrounded by Israeli troops and where 36 babies are at risk of dying because there is no power for incubators.
Israel claims Hamas is using hospitals, which are protected under international law, as their bases.
The war was triggered by Hamas’s brutal surprise October 7 attack on Israel, in which the terrorist group killed 1,200 men, women and children and kidnapped another 240.
Israel launched heavy air strikes for nearly three weeks before sending troops and tanks into the north.
As of last Friday, according to the Hamas-run health ministry, more than 11,000 Palestinians, two-thirds of them women and minors, have been killed since the war began six weeks ago.
In all, some 1.5 million Palestinians – more than two-thirds of Gaza’s population – have fled their homes.