Salvatore Sagues, the global rights body's west Africa researcher, said Monday's bloodshed was a "dramatic escalation" of violence in the country normally seen as a beacon of democracy among often troubled neighbours.
Washington has also urged Wade, who has been in office since 2000, to allow power to pass "to the next generation".
"While we respect the process ... our message to him remains the same: that the statesmanly-like thing to do would be to cede to the next generation," State Department spokesperson Victoria Nuland told journalists.
Riot police fired tear gas to break up a tense, thousands-strong rally on Tuesday in Dakar demanding that Wade drop plans to seek a third term in office.
Thousands had gathered by late afternoon in a square in the working class suburb of Colobane, where tension rose and angry youths hurled rocks at scores of riot police keeping watch from afar.
Iconic singer Youssou Ndour, whose presidential hopes were dashed when the constitutional council rejected his candidacy, took to the stage and gestured encouragingly when the crowd chanted: "Let's march to the palace," referring to the presidency downtown.
The agitated protestors dispersed after police fired tear gas and sprayed water on them, but some youths burnt tyres and engaged in running battles with police in side streets after the square emptied out.
"It’s too late"
An AFP journalist saw a woman with injuries to her leg.
A ruling by the constitutional council that Wade was legally allowed to run has sparked fury among opponents who accuse him of fiddling with the law.
"We have decided to take on oppression, injustice, dictatorship," presidential candidate Moustapha Niasse told journalists, his eyes red from tear gas.
One of Africa's most stable nations, Senegal has been rocked by riots after the court ruling, prompting international calls for calm.
But El Hadj Amadou Salla, minister of state and a senior Wade campaign official, said it was "too late" and that the president's candidacy has already been validated.
The opposition argues that the constitution allows a president to serve only two consecutive terms.
When Wade was voted into office in 2000 after 25 years in opposition and the defeated incumbent bowed out gracefully, Senegal was hailed as a model for the strife-torn continent.
However term lengths were amended in 2008 and Wade says the law does not apply retroactively, which theoretically allows him to serve two seven-year terms from 2012.
"I ask the majority to go out and protest, peacefully, to put an end to this coup d’état," the Grammy-winning Ndour said.
A weakening democracy
He said the judges, who ruled that thousands of signatures handed in by Ndour were invalid, "are afraid of me".
He added: "I hold the majority in Senegal. I am the recourse."
Aside from Wade, the council approved 13 other candidates to run in the election including three former prime ministers and main opposition leader Ousmane Tanor Dieng.
Wade said in an interview with a local news website last on Thursday that he needs three more years to complete his projects, fuelling speculation that he wants to line up a successor.
He has long been accused of trying to position his 44-year-old son Karim Wade - already a super-minister in his cabinet - to fill his shoes.
A US diplomatic dispatch published by WikiLeaks in 2010 warned that Senegal was "a weakening democracy", saying Wade was looking to "open a path to a dynastic presidential succession".