Justice Minister Cheikh Tidiane Sy told lawmakers that Wade had dropped the idea, as they met to discuss constitutional reform amid clashes outside the parliament building between police and protesters.
Under the scheme denounced by Wade's foes, if a presidential candidate and his running mate on a shared ticket won 25 percent of the votes in the first round of an election, they would have been declared the outright winners.
The current arrangement provides for a threshold of 50 percent of the votes for a win in the first round.
The opposition saw the project as a scheme by Wade, who is 85, to avoid a second round of voting and to line up his son Karim for the succession in elections due next February.
Wade currently runs at about 27 percent in the popularity stakes, according to the opposition.
The opposition had announced a "Don't Touch My Constitution" coalition and world-renowned singer Youssou Ndour hit out on Tuesday at an "abuse of authority."