Labour has said it will end power-sharing agreements with the Green Party on local councils, unless its councillors disown the party's newly-adopted policy that Zionism is a form of racism.
Labour says it will give local Green groups seven days to confirm they reject the policy, which was recently approved by Green members at its party conference.
Labour says its ultimatum applies to 19 councils where it shares power with the Greens, either directly or alongside other parties.
The Greens hit back at the move, accusing Labour of meddling and arguing it would be undemocratic for the party to "tell local parties what to do".
The policy motion adopted by members of the Green Party of England and Wales said Zionism was an ideology that supported an "ethnonationalist Jewish state" that had led to the "disenfranchisement and destruction" of Palestinians.
It backed the creation of a "single democratic Palestinian state in all of historic Palestine", which includes modern-day Israel.
It has led to a backlash from Jewish groups, as well as criticism from senior Green figures, including four of its five MPs.
Green leader Zack Polanski, who skipped the conference vote to unsuccessfully campaign for election in a Westminster by-election, has said he wants to see the "imperfect" motion amended in future.
He has however said that "the displacement and genocide of the Palestinian people is clearly underpinned by racist ideology", arguing this was the "substantial part" of the motion. Israel has denied committing genocide in Gaza.
Labour is currently in coalition with the Green Party on local councils in Sheffield, Lewes and Warwick. In other areas, it runs the council as part of a broader coalition alongside other parties.
On Wednesday, Prime Minister Andy Burnham told MPs Labour would not partner with the Greens over the "antisemitic" policy, although Downing Street did not confirm what this meant for local government.
The party has now said it wants all local Labour groups to write to their Green counterparts, demanding "clear and unambiguous" statements rejecting the policy.
Green groups will also be asked to call on their party's "national leadership" to reconsider the policy.
"Where they are unable to provide that assurance, Labour will bring any such local arrangement to an end," the party's chair Bridget Phillipson said.
In response to Burnham's comments, Polanski said: "I'm the only Jewish leader of a political party. I'm a victim of antisemitism every day and I've made it clear Jewish people are welcome in my party."
A Green Party spokesperson said: "For the Labour government to conflate criticism of Israel with antisemitism is disappointing and wrong.
"Trying to tell local parties what to do and who they can work with is undemocratic".
National parties exercise various levels of control over groups of local councillors who wish to do deals to govern locally.
Labour councillors require the approval of its ruling National Executive Committee before entering into local tie-ups.
According to the party's rulebook, local groups must also "stand down" from power sharing arrangements when asked to do so by their regional office.
By contrast, the Green Party of England and Wales allows local groups to make the final decision on where and whether to share power locally.