With little more than three weeks to go before the vote, the unprecedented step followed a formal request to postpone from the opposition Senegalese Democratic Party (PDS), whose candidate was excluded from the running in January.
The constitutional council's decision to exclude prominent contenders such as the PDS's Karim Wade and opposition firebrand Ousmane Sonko has fuelled growing discontent about the election process.
The excluded candidates say the rules for candidacy were not applied fairly. The authorities deny this.
"These troubled conditions could seriously undermine the credibility of the ballot by sowing the seeds of pre- and post-electoral disputes," Sall said in his address.
He did not set a new date for the vote, but said there would be a national dialogue to ensure the election would be free, fair and transparent.
He said the postponement would not affect his decision not to run for a third term - an issue that has helped fuel recurrent unrest in what is normally one of West Africa's most stable democracies.
(Additional reporting by Portia Crowe and Bate FelixWriting by Alessandra PrenticeEditing by Giles Elgood, Mark Potter and Frances Kerry)
By Diadie Ba, Ngouda Dione and Bate Felix
