FILE - Demonstrators against dictatorship and against human rights violations in Senegal protest at the Brandenburg Gaten in Berlin, Germany on February 10, 2024.
Sall's last-minute move to postpone the February 25 poll until December triggered Senegal's worst crisis in decades.
The decision sparked a widespread outcry and deadly protests in what is often seen as a bastion of stability in coup-hit West Africa.
The Constitutional Council's ruling late on Thursday to annul the vote delay plunged the country into further uncertainty.
"The president of the republic intends to fully implement the decision of the Constitutional Council," the presidency said in a statement.
"To this end, the head of state will without delay carry out the consultations necessary to organize the presidential election as soon as possible."
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 2023.
Parliament later approved the delay until December 15, but only after security forces entered the building and removed some opposition lawmakers who opposed the bill.
The vote paved the way for Sall — whose second term is due to expire in April — to remain in office until a successor was installed.
Three people have been killed during demonstrations against the vote delay, with security forces repressing attempts to mobilise.
The ruling by the Constitutional Council was widely welcomed for easing tensions.
By mid-afternoon on Friday, there was virtually no response to calls for protests in the capital Dakar, where police and journalists outnumbered demonstrators, an AFP journalist saw.
The opposition had decried Sall's move as a "constitutional coup," saying his party feared defeat at the ballot box for its candidate Prime Minister Amadou Ba.
Sall's term in office officially expires on April 2 and the head of state has repeatedly said he will not stand for a third term.
The Constitutional Council reiterated the fixed nature of the five-year presidential term.
'Historic'
Senegal had faced growing calls from major international partners to swiftly organize the vote.
The West African regional bloc, ECOWAS, the European Union, France and Britain all called on the authorities to comply with the Council's ruling.
People interviewed by AFP in the streets of Dakar expressed relief at the move.
FILE - A protester throws stones during clashes with police on the sidelines of a protest against a last-minute delay of presidential elections in Dakar on February 9, 2024.
"It's good that the Constitutional Council is taking the decision it has, at least we're halfway to the right solution," said 55-year-old Mamadou Caba.
Babacar Gueye, a constitutional expert and coordinator of a civil society collective which opposed the vote delay, described the Council's decision as "historic."
"The Council did not set a deadline, it simply said 'as soon as possible.' This means both quickly and under the right conditions," said Gueye, one of the organizers of the Aar Sunu Election (Let's protect our election) collective.
The Constitutional Council in January approved 20 candidates to run in the presidential election.
It remains to be seen whether the same list of candidates will be put forward again and when the vote will take place.
Discussions
Government spokesman Abdou Karim Fofana said the Council had not imposed a date, adding that he foresaw discussions between the president and political players "which will enable things to be organized."
The president "must make arrangements for us to discuss and see how to implement the Council's decision," Khalifa Sall, one of the principal presidential candidates, told journalists.
He did not say whether the election should take place before or after President Sall's departure.
But he added that when the president's mandate ends on April 2, Sall "must go."
FILE - opposition candidate Bassirou Diomaye FAYE
Amadou Ba, the representative of detained opposition figure Bassirou Diomaye Faye, said that "Macky (Sall) must organize the presidential election before the end of his mandate," the Walf daily reported.
Faye is the second-in-command of the dissolved PASTEF party, which has been involved in a bitter stand-off with the state since 2021, sparking sometimes deadly unrest.
Hundreds of party supporters and civil society members have been arrested.
More than 130 of them have been released from prison since Thursday and around 90 more are due to be freed on Friday, according to the justice ministry.