People walk past a burned-out car in Dakar, on June 5, 2023, as protestS calmed down. AFP
The June 1-3 violence was sparked by a two-year sentence on opposition figurehead Ousmane Sonko for "corrupting" a young woman, making him ineligible to contest presidential polls next year.
Sonko accuses Sall of trying to install a "dictatorship" at the apex of a corrupt elite.
Around 23 people died, according to Amnesty figures "including some by gunfire", while the government says 16 people perished in the unrest.
"The use of firearms by security forces during protests sets a negative precedent for Senegal," UN rights office spokesman Seif Magango told reporters in Geneva.
He noted that Senegal had launched investigations into the incidents but added that the UN rights office wanted a "prompt, independent and thorough" probe and punishment for those responsible "regardless of their status and political affiliation."
"We offer our office's assistance in this respect."
Sonko, a 48-year-old former tax inspector, has spoken out against debt, poverty, food insecurity, under-funded health and education systems and corruption.
He was initially charged with rape but was convicted on a lesser charge of morally "corrupting" a young woman in a case that lasted two years.
The UN rights office said "at least" 16 people were killed in last week's violence, while 350 were injured and more than 500 arrested during the three days of protests.
"We are also concerned about continuing restrictions on freedom of expression and peaceful assembly in the wake of the protests," Magango said.
He highlighted the situation of private broadcaster Walfadjiri TV, which had been covering the protests live, before it "was suspended on June 1 without clear legal justification and remains off air to date".
The UN rights office also pointed out that internet services had been restricted between June 1 and 6, ostensibly to stop the "dissemination of hateful and subversive messages".
"Internet restrictions must be grounded in unambiguous, publicly available law; must be necessary to achieve a legitimate aim," Magango said.