New Prime Minister Manuel Valls arrived at the Elysée presidential palaace at 8.00am on Wednesday to discuss the make-up of his cabinet with Francois Hollande.
The French president appointed Valls to the post on Monday, replacing Jean-Marc Ayrault, after the Socialist Party suffered losses in local elections over the weekend.
Valls is on the right of the Socialist Party and, although he scores well in opinion polls, his tough line on crime and immigration, including comments that most Roma do not want to become part of French society, has upset the left of the party and the Greens.
On Tuesday Green ministers Cécile Duflot and Pascal Canfin announced they would refuse to sit in a Valls cabinet and later the party's leading body decided to quit the government, despite reportedly being offered some important positions.
The Greens are looking ahead to European elections in May, with an eye to siphoning votes away from the Socialists, EELV member and former MEP Alain Lipietz told RFI.
But several leading party members, including senators Jean-Vincent Placé, André Gattolin and Ronan Dantec and deputies Barbara Pompili, François de Rugy and François-Michel Lambert, advocated sticking with the Socialists.
Lambert declared himself "stunned by the immaturity" of the party, while de Rugy called the decision "incomprehensible".
"We have a divided party, it's worrying for the future," he told Le Monde newspaper.