Small groups from the Sunni Tehrik movement held demonstrations in different Pakistani cities after Friday prayers calling for Asia Bibi, who was convicted of blasphemy by a court in 2010, to be killed.
Her appeal was dismissed by the Lahore High Court in 2014, but the supreme court stayed her execution in 2015 suspending the high court verdict.
Asia Bibi was arrested after she and a Muslim neighbour had a confrontation.
She drank from a cup designated for Muslims, prompting an argument in which she said: "I believe in my religion and in Jesus Christ, who died on the cross for the sins of mankind. What did your Prophet Mohammed ever do to save mankind?"
A mob then beat her and her family, with some reports saying she was also gang-raped.
Anti-Christian feeling has been on the increase in Pakistan amid the increase of extremist Muslims.
In March 73 people were killed and hundreds more injured in a Taliban bomb attack at an Easter celebration in Lahore.