Labour called urgent crisis talks last night, as the party is said to be braced for further resignations over the party's messaging on Israel.
David Lammy and Sir Keir Starmer met with council leaders late last night.
They are said to have demanded Starmer rows back on previous interview comments about potential war crimes in Gaza, instead taking a firmer stance on condemning war crimes.
Sources told ITV that last night's meeting saw Labour councillors also demand that they be allowed to attend pro-Palestine demonstrations.
Over the weekend, Labour MPs and councillors were reportedly told not to attend the demonstrations.
One council leader told last night's meeting that he had more than a dozen councillors threatening to resign over the issue.
This came after Starmer was accused of "endorsing war crimes" through his stance on Israel, with three Labour councillors quitting the party over the issue.
Amna Abdullatif - the first Arab Muslim woman elected to Manchester City Council - resigned from the party this week, accusing the Labour leader of making "horrifying comments" about Palestine.
The Ardwick councillor, who was elected in 2019, said she had been left with "no choice other than to resign the Labour whip and resign from the Labour party due to Keir Starmer and a number of his senior frontbench making horrifying comments about Israel having the right to withhold fuel, water, food and electricity from the 2.2 million Palestinians trapped in Gaza, effectively endorsing a war crime".
In an interview with LBC last week, Starmer that "Israel has the right" to withhold power and water from Palestinian civilians.
But he added: "Obviously, everything should be done within international law".
In a statement posted to X on Saturday, Starmer called on "all parties to act in line with international law, including allowing humanitarian access of food, water, electricity and medicines to Gaza and ensuring safe humanitarian corridors in Gaza for those fleeing violence".
Starmer has made a point of taking a firm stance on the attacks by Hamas, which took place just over a week ago in Israel.
But Abdullatif, who has been a Labour member for 10 years, will now sit as an independent as a result of what she said was an "inhumane" position.
Writing on Twitter, she said: "Collective punishment is illegal under international law. It is inhumane and unconscionable.
"I cannot fathom how the leadership of the party I represent has not called for a de-escalation to violence, and a ceasefire."
The councillor added: "This is deeply irresponsible and dangerous."
Shaista Aziz and Dr Amar Latif - both councillors in Oxford - quit the party last week on similar grounds.
Speaking to the Oxford Mail, Aziz said: "Like all decent-minded people, we are devastated by the atrocities carried out by Hamas in Israel.
"However, we are appalled by the words of Keir Starmer."
She said that an invasion of Gaza by Israel "contravenes international law", adding: "We believe that politicians need to be evoking humanity and calling for an end to collective punishment in Gaza."
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Starmer has made a point of taking a firm stance on the attacks by Hamas, which took place just over a week ago in Israel
PA
Having served as a councillor since 2018, she said she feels "great sadness" at leaving the party.
Lubaba Khalid, who worked as a Young Labour BAME (black and minority ethnic) officer, also handed in her resignation last week.
The Palestinian photographer said she felt "absolutely appalled" by the Labour leader's comments.
She claimed the remarks were "reaffirmed" by shadow attorney general Emily Thornberry, warning that Labour is "no longer a safe place for Palestinians and Muslims."
The Labour Party has been contacted for comment.
