PARIS — Three weeks into an impasse over who won a leadership vote in France’s center-right opposition party, Francois Fillon — who was declared the loser, though he has refused to concede — proposed Tuesday that a new election be held next spring in which he probably would not run.

In a radio interview, Fillon, a former prime minister under former president Nicolas Sarkozy, gave his formal support to an increasingly vocal campaign within the party, the Union for a Popular Movement, or UMP, to hold a new ballot under ground rules to be determined.