"We will accomplish the mission of our great leader and make Pakistan a peaceful democratic and welfare state," Gilani said.
Gilani also announced that, to mark the occasion, death sentences of all prisoners would be commuted to life imprisonment and a 90-day reduction in jail terms would be given to many inmates.
Bhutto's Pakistan Peoples Party has started a week-long blood donation campaign and the government has re-named Islamabad international airport after Bhutto, who was born on June 21 1953.
Asif Ali Zardari, Bhutto's widower and now the chairperson of her party, attended memorial services in her native town of Gharhi Khuda Bakhsh where she was buried in the family mausoleum.
Bhutto's father, former premier Zulfiqar Ali Bhutto, was hanged in 1979 on the orders of military dictator Zia ul-Haq, propelling his daughter to carry on his legacy.
After Zia died in a mysterious plane crash in 1988, Bhutto - at the age of just 35 - became the first female prime minister of an Islamic country.
She was elected twice, and both times she was thrown out of office on allegations of corruption.