Copé rejected demands for a fresh vote after the formal announcement that his rival for the leadership, Francois Fillon, had formed his own faction inside parliament.
The conditions for the formation of an internal party referendum had not been met, said Copé in a statement.
"The red line has been crossed and I am drawing the conclusions from that," he added after the formation of Fillon's parliamentary group was announced in the parliament's official proceedings.
"From now on, I am only going to be the main opponent of (French President) François Hollande."
Copé, an ally of former president Nicolas Sarkozy, had already on Tuesday brushed aside Sarkozy's suggestion — reported by several informed sources — for a fresh ballot.
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"The time is not right in the heat of the moment, in the bitterness . . . to say we must vote again right away," Copé told French radio on Tuesday.
But Fillon, who served as prime minister under Sarkozy, struck back Tuesday after a meeting with his supporters.
They announced the formation of a new parliamentary faction, which would be dissolved as soon as a new vote was held.
Copé's statement on Wednesday however suggests that as far as he is concerned, the dispute is over and it is time to get on with the business of opposition.