"Sudan's security forces must stop their ongoing deadly onslaught on protesters and medical personnel," the London-based group said in a statement.
Demonstrations have rocked Sudan since December 19, when the government raised the price of bread. They have escalated into broad demonstrations against President Omar al-Bashir's three-decade rule.
Bashir has defied calls to step down, and rights groups say security forces have responded with deadly force.
A doctors' committee linked to the Sudanese Professionals Association (SPA) that is spearheading the protest movement said a child and doctor were killed by live ammunition Thursday during demonstrations in the capital Khartoum.
An SPA spokesman said later that another protester had also died during the day.
Sudanese officials have not confirmed the three deaths, but earlier said 24 people had died in protest-related violence since December.
Amnesty said last week that over 40 people have been killed in the unrest, with more than 1,000 arrested.
Sarah Jackson, Amnesty's deputy director for East Africa, said Friday it was an "outrage that Sudanese security forces continue to use lethal force on protesters and key service providers like doctors".
She accused security personnel of "killing people in an unbridled spree that is even affecting children".
Amnesty has reported repeated raids on medical facilities by the security forces, saying they have fired teargas and live bullets inside hospitals as well as arresting and beating doctors.
"By participating in these protests, the people of Sudan are exercising their legitimate rights to freedom of expression and peaceful assembly," Jackson said Friday.
"Instead of trying to curtail these rights, the government should address the root causes of the economic crisis that has driven the people to the streets."
In a separate statement Human Rights Watch also called on the government to "immediately release or charge those detained in relation to the ongoing protests".
"Those arrested include protesters, journalists, doctors, lawyers, and opposition party leaders," a statement said.
The group said the number of people detained was "most likely far greater" than the official figure of 816 given on January 7.
"Many of those arrested remain in incommunicado detention, without access to family or lawyer visits," it said.
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