Sall has faced a clamor to set a date for the vote after his abrupt delay to the February 25 election triggered weeks of crisis.
Amid simmering social and political tensions, the president put off a decision on the date until after a political dialogue due to begin on Monday.
In an apparent move to pacify public opinion, Sall also said he would consider releasing imprisoned opposition figures Ousmane Sonko and Bassirou Diomaye Faye.
"On April 2, 2024, my mission ends as the head of Senegal," the president said, seemingly ending suspicions that he might remain in office longer than expected.
"As far as the date is concerned, we'll see what the dialogue comes up with," he added during a televised press interview.
FILE —People watch the Senegal's President Macky Sall during a live press conference broadcast on the national television, in the district of Medina in Dakar on February 22, 2024.
"The election can be held before or after April 2," he said.
But when pressed, he added that he did not think it would be possible before April 2.
Sall said he would hold discussions on Monday and Tuesday with presidential candidates and other political and social actors.
"At the end of the dialogue, we must have a date," he said.
Sall announced the election delay hours before official campaigning was due to begin. Parliament backed the move, despite strong opposition, and Sall then set a new election date in December.
The opposition denounced Sall's move as a "constitutional coup," saying his party feared defeat at the ballot box.
The delay plunged the traditionally stable West African country into a political crisis and sparked unrest that has left four people dead.
Senegal's top constitutional body last week overturned the delay and called for the vote to be organised "as soon as possible."
During a cabinet meeting Wednesday, the president said the election date "will be set very soon," according to the presidency.
'Dialogue'
During Thursday's interview, Sall said he was considering a pardon or an amnesty law for former adversaries.
He said he would consider the release opposition figure Ousmane Sonko, who has been in jail since last July on charges including calling for insurrection.
FILE —Senegalese opposition leader Ousmane Sonko addresses journalists following his release from police custody in Dakar, Senegal, on March 8, 2021.
"I am ready to go that far so that everyone can benefit from this pardon and so that Senegal can move towards these elections in a peaceful manner," Sall said.
Sonko has a passionate following in the country with his pan-Africanist and socialist views and tough stance on former colonial power France.
Speaking of opposition figure Bassirou Diomaye Faye, who is a contender for the presidency despite being in jail, Sall said that "before these laws come into force, he may be granted provisional release to respond to the call for dialogue."
Sall had previously said he wanted dialogue to calm tensions and asked the justice ministry to finish draft legislation to follow through on "the will for reconciliation and forgiveness."
Hundreds of detained opposition and civil society members were released last week.
However, civil society groups have called another rally for Saturday in the capital Dakar to keep up the pressure, after mobilising several thousand people last weekend.
Faye on Wednesday accused Sall of dragging his feet.
His criticism echoed that of most other candidates who accused Sall in a joint statement of "ill will."
Faye said in a statement he would only agree to talks on an election date "without delay" and before the end of Sall's term.
Sall, who has been in power since 2012, said he called off the vote over disputes about the disqualification of potential candidates and concern about a return to unrest seen in 2021 and last year.
The opposition accuses him of trying to remain in office, though Sall has repeatedly said he will not stand for a third term.