There were fears Wednesday's banned protest would mirror similar nationwide demonstrations that turned violent on June 17 as police fired tear gas and water cannon to disperse crowds. Three people were killed during the protest.
Some social media users had voiced concern about repercussions of more unrest on the upcoming holiday, locally known as "Tabaski", when families traditionally slaughter a pricey ram for a feast and have new clothes made.
The protest could also have disrupted plans by those preparing to travel for the annual Hajj Islamic pilgrimage to Mecca, which many in the Muslim-majority country join each year.
"We have to listen to the people," Sonko told a news conference in the capital Dakar hours before protests were meant to kick off.
"We have received messages and calls, so taking into account pilgrimages (to Mecca), exams, and Tabaski, we are postponing the demonstration," he said.
Another member of the Yewwi Askan Wi coalition, Aida Mbodj, said the postponement would benefit tailors and other businesses that see an uptick in business ahead of Tabaski.
Tensions have run high in Senegal since major protests broke out last year after Sonko was arrested on rape charges, which he denied.
Many accuse Sall, who came to power in 2012, of trying to eliminate his competition and clearing the field to run for a third term, which he has neither confirmed nor denied.
Anger flared again after Yewwi Askan Wi's proportional national candidate list was disqualified from a July 31 legislative election on technical grounds.
During the past week, Sonko supporters responded to calls for a different kind of protest: banging post and pans together at 8 p.m. from windows and balconies. (Full Story)
The opposition leader invited the public to join another 30-minute "mass saucepan concert" on Thursday.
"The Senegalese (people) have a chance to end debates around the third term without any deaths," he said. "We need the people to vote massively against Macky Sall on July 31."