Officer Iqbal Khan says the bomber struck a Tuesday night rally for Haroon Ahmed Bilour, an Awami National Party candidate for a provincial seat.
Aside from Haroon Bilour, others killed in the explosion have been identified as Asif Khan, Muhammad Shoaib, Muhammad Naeem, Yaseen, Haji Muhammad Guk, Najeebullah, Abidullah, Huzaifa, Arif Hussain, Akhtar Gul, Imran, Rizwan, Zameer Khan, Asrar, Sameen, Sadiq, and Khan Muhammad.
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.
Overall, violence in Pakistan has decreased in recent years after several military offensives against militant strongholds in the northwest.
The Election Commission has delayed the election on Peshawar's PK-78, from where ANP leader Haroon Bilour was contesting. His father, Bashir Bilour, also a prominent ANP politician, was killed by a suicide bomber in 2012.
On July 4, NACTA Director Obaid Farooq while briefing a sub-committee of the Senate Standing Committee on Interior had said, "We have received as many as 12 threat alerts which are about leadership of political parties, including the Pakistan People's Party (PPP) and Pakistan Muslim League-Nawaz (PML-N), and six personalities can be targeted during elections". Mr Bilour was taken to hospital but later succumbed to his injuries. Police and bomb disposal officials collected evidence from the site of the blast and initiated an investigation into the incident.
The body of Haroon Bilour was later shifted to Bilour House where ANP workers gathered in great numbers to pay respect to their deceased leader.
The death toll is feared to go up as some of those injured in the explosion are in critical condition.
Claiming responsibility for the attack, Tehreek-e-Taliban Pakistan (TTP) spokesperson termed the assasination "revenge for ANP's previous government". Emergency was declared in all the hospitals of the city.
People took to the social media to show solidarity with the victims of terrorism soon after the tragic news broke.
"Political differences apart, all political parties and their candidates must be provided proper security during their election campaigns by the state", he said in a tweet.
The bombing came hours after the Pakistan military spokesman said there were security threats ahead of national elections scheduled for July 25.