Sall has faced an uproar since he pushed back the vote scheduled for February 25, triggering one of the West African nation's worst political crises.
The Constitutional Council overturned the delay and called last week for the vote to be held "as soon as possible."
But Sall appears in no hurry to set a date to elect his successor before his term ends on April 2.
He has put off the decision until after talks with political and social actors from Monday and hopes to reach an agreement by late Tuesday.
That has left the Senegalese people in the dark as to when they will be able to vote and created a political clamor for the elections to take place soon.
Saturday's opposition protest saw hundreds answer the call of the F24 grouping to gather on a sandy open space in a working-class quarter of the capital.
FILE —Supporters of presidential candidate Bassirou Diomaye and opposition leader Ousmane Sonko demonstrate in Dakar on February 24, 2024.
"We want elections," protesters chanted, draped in national flags and calling Sall a "dictator."
Ibrahima Niang, a 34-year-old refuse collector, told AFP he was "demonstrating for one thing:" the release of jailed opposition figurehead Ousmane Sonko.
Sall criticism 'totally false'
A few hours afterwards, a boisterous pro-Sall crowd draped in Senegalese national colours marched in a residential area of Dakar.
Mamadou Dia, a 30-year-old student, defended Sall's record as president since 2012 and believes the election date matters little.
"We are here to show national and international opinion that what people are saying about Macky Sall is totally false. Macky Sall has done all he needed to do for Senegal," he said.
FILE —Supporters of Senegal's current President rally to support their leader in Dakar on February 24, 2024.
In an apparent move to pacify public opinion, Sall has said he would consider provisional releases, pardons or an amnesty law for opposition figures including Sonko and his deputy Bassirou Diomaye Faye, who is also in jail.
According to Sall, he delayed the election because of disputes over the disqualification of potential candidates and concerns about a return to unrest seen in 2021 and last year.
Most of the candidates for president and a large civil society collective have announced they will refuse to take part in the talks Sall intends to stage.
"We oppose all proposals for dialogue and demand that a date be set before April 2," Boubacar Camara, among the group of 16 candidates, said Friday.
'Attempt at diversion'
If no agreement is reached during the dialogue, Sall said it would be up to the Constitutional Council to decide the next step.
He stressed that his mandate would end as planned on April 2.
FILE—Supporters of Senegal's president Macky Sall march in support of him after the postponement of the February 25 presidential election and ahead of a national dialogue proposed by Sall, in Dakar, Senegal, February 24, 2024.
But he left open the question of when the vote would take place, adding later that he did not think it would be possible before April 2.
The Aar Sunu Election (Protect Our Election) collective of 40 Senegalese civil society groups also rejected Sall's dialogue offer, describing it as an "attempt at diversion."
"Our position is (before) April 2, otherwise there will be a crisis," said Malick Diop, one of the collective's organisers.
Aar Sunu Election mobilised several thousand people in the capital Dakar last weekend.
The opposition has denounced Sall's last-minute move to delay the vote as a "constitutional coup," saying his party feared defeat at the ballot box.
The election chaos has plunged the traditionally stable West African country into turmoil and sparked unrest that has left four people dead.
Dakar's Cheikh Anta Diop University, an opposition stronghold that was closed following unrest around Sonko's jailing last year, announced it would reopen on Monday.