The presidential election had been set for February 25 and Sall has not announced any new date, sparking a wave of criticism from opposition leaders and international concern.
In his statement Saturday, Sall said he was intervening because of a dispute between the National Assembly and the Constitutional Court over the rejection of candidates.
Lawmakers are investigating two Constitutional Council judges whose integrity in the election process has been questioned. Sall promised to ensure "a free, transparent and inclusive election," but did not set a new date for the vote.
On Sunday, hundreds of men and women took to the streets, answering the call of some opposition leaders.
Waving Senegalese flags or sporting the jersey of the national football team, they converged in the early afternoon at a roundabout on one of the capital's main roads.
Police, some on foot and others in pick-up trucks, responded with tear gas and then pursued the fleeing protesters through adjoining streets, while some demonstrators responded by throwing rocks.
Youths shouting "Macky Sall, dictator!" set up makeshift barricades and burned tyres in the streets.
'Constitutional coup'
Former prime minister Aminata Toure, now a leading opposition figure, was arrested while arriving at one protest.
FILE - Aminata Toure, former Prime Minister of Senegal and incoming Member of Parliament, poses for a portrait in her house in Dakar, on September 8, 2022.
She posted on X, formerly Twitter, that she had just been detained, which opposition deputy Guy Marius Sagna confirmed to AFP. Toure served as prime minister under Sall before joining the opposition and becoming one of his most outspoken critics.
She had denounced his decision to postpone the election as an "unprecedented democratic regression" in a post on X Saturday.
Another presidential candidate, Daouda Ndiaye, posted on social media to say he had been beaten by the security forces.
AFP was unable to confirm reports that another opposition leader and presidential candidate Anta Babacar Ngom had also been detained.
Images posted on social media appear to show her struggling with members of the security forces.
Later Sunday, the communications ministry ordered private broadcaster Walf TV off air, saying its coverage of the protests amounted to "incitement to violence." Walf announced on social media that its licence had been withdrawn.
Opposition leaders and presidential candidates have lined up to denounce Sall's decision.
Habib Sy, one of the 20 candidates, said opposition parties had agreed to launch their election campaigns together despite the official postponement.
FILE - Supporters of opposition candidate Khalifa Sall gather outside his party headquarters ahead of the demonstrations called by the opposition parties in Dakar on February 4, 2024, to protest against postponement of the presidential election.
Another opposition figure, former mayor of Dakar Khalifa Sall, called for pro-democratic forces to unite. "All of Senegal must stand up," he told journalists.
Sall, who is not related to the president, denounced "a constitutional coup" by a leader who "dreams of eternity."
Under Senegal's election code, at least 80 days must pass between publication of the decree setting the date and the election, so the earliest a vote could now be held is late April.
International concern
The United States, the European Union and former colonial ruler France led appeals for the vote to be rescheduled at the earliest date.
The EU called for a prompt, transparent, inclusive and credible election, spokesperson Nabila Massrali noting that the delay "opens a period of uncertainty."
France's foreign ministry urged authorities to "end the uncertainty... so the vote can be held as soon as possible."
The US State Department, one of the first to react, called on Senegal to set a date for a "timely, free and fair election."
The West African bloc ECOWAS issued a statement expressing concern and calling for dialogue.
Senegal has traditionally been seen as a rare example of democratic stability in West Africa, which has been hit by a series of coups in recent years in Mali, Niger and Burkina Faso.
There had been 20 candidates in the running, although two major opposition figures had already been excluded.
President Sall on Saturday reiterated that he would not be a candidate.
Excluded candidates
Sall had designated Prime Minister Amadou Ba from his party as his would-be successor.
FILE - Senegal Minister of Economy, Finance and Planning Amadou Ba at an annual meeting of the International Monetary Fund and World Bank October 6, 2016 in Washington, DC.
But with the party split over his candidacy, Ba faced possible defeat in the ballot box.
Anti-establishment candidate Bassirou Diomaye Faye's candidacy was approved by the authorities, despite the fact that he is currently behind bars.
But the Constitutional Council has excluded dozens of candidates from the vote, including opposition leader Ousmane Sonko, who has been jailed since July 2023, and Karim Wade, son of former president Abdoulaye Wade.
Wade's supporters in the National Assembly called for a parliamentary inquiry into the partiality of two judges on the Constitutional Court.
That motion was passed by the Assembly on January 31, with some members of Sall's party supporting it.