The 25-year-old Bilawal said the PPP was not like the Pakistan Tehrik-e-Insaf led by the "cowardly" Khan.
He told a group of charged supporters here that Khan "stood outside a church and made excuses for the terrorists who were responsible for the attack" in Peshawar that killed over 80 people on September 21.
He was referring to the attack on All Saints Church in Peshawar by two suicide bombers that was claimed by a Taliban faction.
The PPP is a party of "courageous and martyred" leaders that is not afraid of terrorists, he said.
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Bilawal made the remarks while addressing a meeting organised here by the PPP to mark the anniversary of the 2007 suicide attack on his late mother Benazir Bhutto's motorcade that killed over 140 people. Bhutto survived that attack but was killed two months later by a suicide bomber.
In recent days, Bilawal and Khan's supporters have had several heated exchanges on Twitter. Lauding teenage rights activist Malala Yusufzai, Bilawal tweeted that she puts Khan to "shame coz at 14 she had courage to talk against (the Taliban) but (Khan) is a coward at 60".
"In the 2018 elections, Asif Ali Zardari will be the jiyalas' bow and I will be the arrow," he said. The PPP's supporters are known as "jiyalas".
He assured the People that he would fight and give his life for them. If a person lost his brother or son to acts of terrorism, then he would take their place, Bilawal said.
He also declared a jihad against religious extremists and pledged that the southern Sindh province would remain the PPP's stronghold.