A foreign news agency cited a police officer, Iqbal Khan, as saying that the bomber struck a Tuesday night rally for ANP candidate Haroon Ahmed Bilour.
The ANP and its ally the Pakistan Peoples Party were unable to campaign for the last general election in 2013 because of threats and attacks on their events and supporters by terrorist groups like the Pakistani Taliban.
The ANP leader's funeral prayers will be offered at Wazir Bagh Peshawar at 5:00 pm on Wednesday.
Chief Election Commissioner Raza Khan said the attack on an electoral candidate, despite the ECP's directions to provide security, was a result of the security institutions' negligence.
Haroon Bilour was one of the ANP's election candidates and belonged to an influential political family in the Khyber-Pakhtunkhwa province, of which Peshawar is the capital.
Local television channels broadcast live scenes of ambulances arriving at the site and rushing victims to the hospital.
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Following the incident, the Election Commission of Pakistan postponed the polls in PK-78 constituency. Bilour's father, Bashir Ahmed Bilour, was killed by a suicide bomber during a meeting in 2012 ahead of the election.
A report claimed that 8 kilos TNT explosive was used in the blast.
Condemning the attack, Pakistan Tehreek-i-Insaaf (PTI) chief Imran Khan condoled Bilour's death stating that it was "Sad to learn of Haroon Bilour and 2 other ANP workers deaths and strongly condemn the terrorist attack at the ANP corner mtg in Peshawar".
Terming it the "peak of terrorism", ANP leader Mian Iftikhar Hussain said the attack is aimed at derailing democratic system in the country and a conspiracy to delay upcoming general elections. "We were waiting at the venue when we heard an explosion as soon as Bilour's vehicle approached the gate", he said. More than 380,000 personnel will be deployed for the elections, according to Major General Asif Ghafoor, the military spokesperson.
The ANP is a predominantly secular, ethnic Pashtun nationalist party, which has long competed with Islamist parties for votes in Pakistan's volatile Pashtun lands, along the border with Afghanistan.
There was no immediate claim of responsibility for Tuesday's attack. Officials have said that while the threat remains, militants have been significantly weakened because of military operations in recent years. The outlawed TTP had claimed responsibility for that attack.