He also announced to call of his 'jalsa' (rally) in Peshawar which was scheduled to take place on Thursday.
"In solidarity with the Bilour family
ANP I've suspended my political activities for today and Peshawar jalsa which was to be held tomorrow. Join ANP in reaffirming elections should be held on time," Bilawal tweeted.
The Bhutto scion also expressed his condolences, grief and outrage at the assassination of Haroon Bilour who is the son of Bashir Bilour, the ANP politician who was killed in 2012.
"Lost for words to express condolences, grief and outrage at the assassination of Shaheed Haroon Bilour son of Shaheed Bashir Bilour. Never ending cycle of national tragedies must ultimately lead to the necessary consistent consensus on combating violent extremism," he wrote in another tweet.
Tuesday's bombing targeted a political rally of the Awami National Party (ANP).
The Tehreek-e-Taliban Pakistan (TTP) has claimed the responsibility for the attack.
Bilour was the ANP's candidate for a provincial seat (PK-78) in the upcoming general elections on July 25.
The explosion occurred in YakaToot neighbourhood on Tuesday night, moments after Bilour arrived at the venue to address supporters at the meeting.
Condemning the incident, Pakistan Tehreek-e-Insaf (PTI) chief Imran Khan sought security for the political parties and their candidates during the election campaigns.
"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. All political parties and their candidates must be provided proper security during their election campaigns by the State," Khan tweeted.
Meanwhile, Pakistan Muslim League-Nawaz (PML-N) President Shahbaz Sharif called the incident "a barbaric act."
"Shocking news from Peshawar: Grieved to learn about shahadat of Haroon Bilour. Strongly condemn this barbaric act of terrorism on a public meeting. Its govt
ECP's responsibility 2 provide fool-proof security 2 political parties leaders. My condolences to bereaved families
The ANP was the main target of Taliban attacks in the 2013 general elections. (ANI)