"People were killed at the (Lekki) tollgate by security forces," Amnesty's Nigeria spokesman Isa Sanusi told AFP, in reference to a key protest site in the city.
He said the rights group was "working on verifying how many".
Witnesses told AFP that shots were fired at the crowd of over 1,000 peaceful demonstrators to disperse them several hours after the authorities declared an open-ended lockdown in Lagos in the face of spiralling protests.
"We were all sitting down, peacefully, and they shut down the lights and the billboards, everyone started screaming," a protester called Toye told AFP, asking that her full name not be used.
"They came to us, but I don't know who it was. They were shooting, and everyone was running for his life."
Another protester, Innocent, said he was helping to ferry the wounded to nearby hospitals.
"Currently I have two people that I rush in my car, a woman and a guy, who are in very critical conditions," he said.
"I rushed two people already to hospital. One was shot at the back, and one was shot at the stomach." .
Scenes of people removing a bullet from someone's wound and pleading for help were broadcast in a live video by DJ Switch, a popular disc jockey, to 150,000 Instagram viewers.
Earlier defiant protesters at the scene had sung the national anthem and pledged to remain out on the streets despite the stay-at-home order.
Anger over abuses by the police's loathed Special Anti-Robbery Squad (SARS) erupted into widespread protests some two weeks ago that drew thousands onto the streets.
Lagos state governor Babajide Sanwo-Olu ordered the round-the-clock shutdown in the sprawling economic hub on Tuesday, claiming the protests had "degenerated into a monster" as violence flared in a string of cities.
"Criminals and miscreants are now hiding under the umbrella of these protests to unleash mayhem," he wrote on Twitter, insisting that only essential workers should stay out on the streets.
"We will not watch and allow anarchy in our dear state."
As the tone hardened from the authorities, Nigeria's police chief ordered anti-riot units deployed around the country.
"The force will henceforth exercise the full powers of the law to prevent any further attempt on lives and property of citizens," a statement said.
Up until Tuesday some 18 people had died in the demonstrations as clashes were reported between protesters and assailants wearing civilian clothes.
Rights groups and demonstrators have accused "thugs and sponsored hoodlums" of attacking the peaceful rallies and seeking to discredit the protest movement.
Witnesses told AFP that a police station was set ablaze in the Orile Iganmu district of Lagos on Tuesday morning. They said police opened fire on protesters, wounding several.
In the capital Abuja, security forces violently dispersed crowds during the day on Tuesday and thick black smoke could be seen over the city.
Violence spread as well to the largest northern city of Kano as hundreds of people went on a rampage, burning vehicles and looting businesses according to an AFP reporter at the scene.
"The mob came near the school and began assaulting parents who had come to pick up their children," 35-year old auto mechanic Sadiq Mohammed told AFP.
Police said 12 suspects were also arrested in southern Benin city in connection with separate attacks on two police facilities.
The government announced the scrapping of the SARS unit and a raft of reforms over a week ago, but the bid to placate the protesters has failed.
Officials have called for the demonstrations to be suspended to give the authorities time to make good on their pledges.
Nigeria -- where the median age is 18 -- is a tinderbox of profound economic and social grievances.
Around half of the population of 200 million is estimated to live in extreme poverty and unemployment is widespread among the youth.
Africa's biggest oil producer is currently facing a recession as the fall in crude prices sparked by the coronavirus pandemic has battered government finances.
The Lagos Chamber of Commerce said in a statement that estimated economic losses in the past 12 days were at 700 billion naira ($1.8 billion dollars, 1.5 billion euros).
On Tuesday, the Senate called on President Muhammadu Buhari to address the nation on the protests "as a matter of urgency".