The Greens are being tipped to run Brighton and Hove City Council after three Labour councillors quit, with two of them accused of anti-Semitism.
Kate Knight and Nichole Brennan have resigned from the Labour group.
Brighton and Hove City Council said a number of complaints had been made to the national Labour Party over Ms Knight’s Facebook activity.
The resignations come five days after Anne Pissaridou was suspended from the Labour Party over social media posts.
Labour now has 18 seats, compared to the Greens’ 19 councillors.
A joint statement from the leaders of the Labour, Green and Conservative groups on the council said they “recognise that by custom the largest elected group” leads the council, and they were “looking at the best options to ensure a smooth transition of any changes to the current administration”.
The formation of a new administration is expected to be discussed at a full council meeting on Thursday.
Ms Pissaridou was suspended from the Labour Party and later resigned from her position as chair of the council’s environment, transport and sustainability committee.
She remains a member of the Labour group but is barred from attending meetings or speaking on behalf of the group, the council said.
Ms Knight and Ms Brennan both resigned from the Labour group to sit as independents on the council.
Brighton Council would give no more information on the circumstances surrounding Ms Brennan’s resignation.
The Green Party said: “It is clear neither party can claim a majority to lead our city alone.
“We understand Labour are still divided and that some councillors have made clear their unwillingness to support a Green-led council. Residents will have no time for the luxury of parties debating ‘seizing power’.
“Greens are keen to engage with our party membership, the Labour group and all partners to find the best way forward.”
‘Shame on the party’
In a statement, the council’s Labour group said: “It is only right that Labour step aside and allow the Greens to form a new administration. This is in the interest of democracy and in the best interests of the city.”
The council’s former Labour leader, Nancy Platts, said it brought shame on the whole Labour Party to see Ms Knight’s posts.
“On behalf of the Labour group, I am truly sorry to the Jewish community for the hurt these posts have caused.”
She said the Labour group would establish a code of conduct for all councillors to include an emphasis on social media and the importance of recognising anti-Semitic posts.
The statement from Ms Platts, Green leader Phélim Mac Cafferty and Conservative leader Steve Bell said they were “working in the best interests of all in Brighton & Hove to provide stability following the recent resignations”.