President Francois Mitterrand, who steamrolled to re-election over conservative Premier Jacques Chirac, faces the task of forming a new Socialist-led government while the right controls the parliament.

Chirac offered to resign on Tuesday and was awaiting a response from the Socialist president, sources in Chirac's office said Monday.Chirac lost to Mitterrand in runoff voting Sunday. Final results from the Interior Ministry showed Mitterrand with 54 percent of the vote to Chirac's 46 percent.

The leading candidate to succeed the premier appeared to be Michel Rocard, a former agriculture minister and Socialist Party member. Other possibilities were former finance ministers Jacques Delors and Pierre Beregovoy.

The sources in the premier's office, speaking on condition of anonymity, said Chirac's chief of staff Maurice Ulrich called Mitterrand's advisers to propose to transfer the reins of government on Tuesday afternoon.

Reporters who gathered at Chirac's Hotel Matignon offices on the Left Bank saw aides busily packing up files in cardboard boxes and plastic sacks, to clear the way for the new premier's staff.

Mitterrand, 71, is the first president elected twice by popular vote. Charles de Gaulle was elected in 1958 and 1965, and two other men served twice. But before a 1962 constitutional amendment, French presidents always were chosen by indirect election.

Unlike 1981, when Socialists danced at the Bastille to mark a historic victory for the left, victory celebrations this year were subdued. Mitterrand supporters did honk their car horns along the Champs-Elysees.