Thousands of people, including children, had travelled to the Bhutto family mausoleum to pay homage.
Bhutto was assassinated in 2007 in a gun and bomb attack at an election rally in Rawalpindi.
Many wailed and wept as others recited from the Quran and prayed.
Yousuf Raza Gilani, the prime minister, along with his cabinet members also visited the mausoleum.
Zardari's Pakistan Peoples Party (PPP) formed a coalition government after the February 2008 general elections and later forced former president Pervez Musharraf to resign under threats of impeachment.
Zardari then became the president but faced criticism after few months in office for holding onto the sweeping powers he inherited from Musharraf as well as for a controversial amnesty that shielded him and his aides from corruption charges.
Musharraf had issued the decree, known as National Reconciliation Ordinance, as part of a power-sharing deal with Bhutto.
The supreme court scrapped the amnesty on December 16, reopening the cases against more than 8,000 beneficiaries, including Zardari who now enjoys presidential immunity against prosecution.
Plea to quit
Several leaders of the PPP's main rival, the Pakistan Muslim League-Nawaz, and civil rights activists have asked Zardari to relinquish the charge on moral grounds.
Even before the amnesty collapsed, Zardari suffered from abysmal approval ratings, fuelled by his nickname "Mr 10 Per Cent" owing to graft allegations and 11 years spent in jail on charges ranging from corruption to murder.
"The man who spent 11 years in jail, does not care about your threats," Zardari told his supporters on Sunday.
"One should not take our patience as a weakness.
"There are only two places for Asif Ali Zardari - either president or prime minister house or jail."