He voiced "confidence that the next phase of counting of votes will also be completed smoothly," and reiterated the determination of the caretaker government to hand over power to the winners without delay.
More vote-rigging claims
The leader of the governing Pakistan People's Party, Taj Haider, alleged vote rigging in some constituencies in Sindh province and its capital, Karachi, in a news conference broadcast by CNN affiliate Geo TV. Haider called on the country's Election Commission to hold a new vote in the affected constituencies.
Leaders of the Sindh-based Muttahida Quami Movement, one of Pakistan's largest and most liberal parties, told reporters that they would boycott the elections over allegations of rigging.
The Sunni Ittehad Council and Jamaat-e-Islami parties also announced a boycott, Geo TV reported.
Many Pakistanis hope the polls will usher in reform in a country battling issues including corruption, a struggling economy and security threats.
President Asif Ali Zardari condemned Saturday's election violence but said the militants' "cowardly acts" would not stop people from exercising their right to vote.
An open letter from Malala Yousafzai, the Pakistani schoolgirl who was attacked by the Taliban last year for her efforts to promote girls' education, urged everyone, and particularly women, to use their votes.
"If we want education, electricity and natural gas in our country, we must take a step," said her letter, published by Pakistan's Dawn website. "Let's vote for our country. We never realized how much powerful our vote is. One vote can change our country."
Blasts target voters
In some cities, the insecurity was evident Saturday.
Two of the blasts in Karachi targeted the Awami National Party office, killing 11 and wounding 36, said Naeem Shah, a spokesman for Karachi police.
A third explosion was in the Karachi suburb of Landhi. It killed three people and wounded nine, according to the deputy commissioner of Malir district, Qazi Jan Mohammed. Voting continued afterward, he said.
A fourth explosion, which wounded four people, was in the Peerabad area of Karachi, Shah said.
Fakhruddin Ebrahim, the chief election commissioner for Pakistan, said he contacted the military over security concerns in Karachi and the harassment of polling station staff in the city. He said polling material was stolen in several areas.
Eleven people were killed in two separate bombings in Pakistan's volatile Balochistan province, district police officer Allauddin Kasi said. One of the attacks was on a vehicle carrying voters who had cast their ballots, he said.
Another targeted independent candidate Khadim Shah, the prime minister's office said in a statement condemning the bombing.
Elsewhere in Balochistan, at least four people were killed and eight injured in a clash between two groups at a polling station, police official Sardar Muhammad said.
In another incident, 12 Awami National Party supporters were hurt by a hand grenade thrown at a party electoral office in Quetta, said Syed Mobeen Ahmed, a deputy inspector general of police.
Brig. Muhammad Abdur Raheem, the military spokesman for Balochistan, said polling still went well in the province apart from interruptions caused by a few incidents. There was a good turnout, including by women voters, he said.
In the northwestern city of Peshawar, 12 people, children among them, were wounded when a bomb exploded at a polling station in a school, said Habibullah Arif, a local deputy commissioner.
Of the 86 million voters registered to cast ballots, there were 36 million new voters, according to the Election Commission of Pakistan.
There are more than twice as many women candidates as five years ago, with 161 running, compared with the 64 who contested the 2008 poll, according to the United Nations.
As the nation makes the transition after years of mostly military rulers, the economic, political and security situation remains unstable.