Andy Burnham has said he will not support his party forming a partnership with the Green Party as long as it maintains a policy of defining Zionism as a form of racism.
Speaking in the House of Commons, the prime minister said the motion, backed by Green members at its party conference earlier this month, was "wrong" and "antisemitic" and Labour would have "nothing to do with it".
The motion said Zionism was an ideology supporting "an ethnonationalist Jewish state in historic Palestine to the exclusion and/ or domination of the non-Jewish population".
It was criticised by Jewish groups, as well as four Green MPs and two former leaders, one of whom said it was "dangerous" and "divisive".
Party leader Zack Polanski has said the motion was "imperfect" and that he had wanted to see it amended.
However, he has defended the substantial part of the motion arguing that "the displacement and genocide of the Palestinian people is clearly underpinned by racist ideology" was "obvious". Israel has repeatedly denied its actions in Gaza amount to genocide.
The motion, having been backed by members, has become party policy but will not necessarily be included in the party's manifesto at the next general election.
The subject was raised during Prime Minister's Questions, when Conservative MP Dame Harriett Baldwin urged Burnham to "rule out co-operating" with the Green Party.
Burnham replied: "Can I condemn the motion that was passed unequivocally.
"It is wrong, it is antisemitic, and this side of the House will have nothing to do with it.
"We will always take the right response when it comes to any partnerships we have with other parties.
"We cannot support a partnership with a party that holds the position that has recently been adopted."
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.
"You're a prime minister who arms a genocide and locks pensioners up for opposing it."
He added that the "blurring of challenging Israel and antisemitism" was "dangerous and irresponsible".
Labour is currently in coalition with the Green Party on local councils in Sheffield, Lewes and Warwick. In more than 10 other areas, Labour run the council with the Greens as part of a broader coalition.
A Downing Street spokesman would not confirm if the prime minister's position extended to local areas or just applied to national government level.
The adoption of the motion has prompted some Green Party figures to call for changes to the party's rules.
Last week, MP Ellie Chowns told the BBC: "I think it is clear that if we have policy, such significant and damaging policy, made by a vote of just 0.4% of our members, that something isn't working in our structures and our policy-making process."
Members of the Green Party of England and Wales endorsed the policy motion by 1,022 votes to 813 - a small fraction of the 230,000 members in the party.
Key backer of the motion Lubna Speitan has defended the motion arguing that it aimed to oppose "racist systems of oppression" adding: "We stand united against all forms of racism and discrimination - no exemptions."