The office of Exilarch was at this time confronted by a dangerous adversary in the person of the passionate and ambitious gaon Mar Kohen-Zedek (in office 917–936), who attempted to make the Academy of Pumbedita the only center of the Babylonian Jews, thereby threatening the existence of the sister academy of Sura.
He, as well as the Academy of Pumbedita, refused to recognize David as exilarch, whereupon the latter, who was equally resolute and ambitious, deposed Kohen-Ẓedeḳ and appointed another gaon.
This dispute lasted for two years, until Nissim Naharwani, highly respected for his piety, intervened and reconciled the adversaries, peace being concluded at Sarsar (half a day's journey south of Baghdad).
Kohen-Ẓedeḳ and his college accompanied the exilarch as far as Baghdad (in the fall of 921); David ben Zakkai, in turn, recognizing the former as gaon of Pumbedita.
David shrank from nothing which might strengthen his position, and misused his influence in order to extort large contributions from the community.
David deposed Saadia from office and banished him, appointing in his place the insignificant Joseph b. Jacob b. Satia.
David took part in the controversy with Ben Meïr in regard to the fixing of the calendar; and he was one of those who excommunicated the agitator (see "Rev.