Balochistan Awami Party candidate Nawabzada Siraj Raisani, who was scheduled to contest the election against his brother, died in the blast.
Akram Durrani, former chief minister of the province of Khyber-Pakhtunkhwa, was unhurt in the bombing, which struck his rally in the town of Bannu, local police chief Kurram Rashid said.
ISIS's AMAQ news agency provided no further detail or evidence for its claim.
Police had earlier said more than 1,000 people were in attendance at the rally.
"Seventy bodies are in six different hospitals and there are more than 120 wounded".
Friday's deadly attack in the Balochistan province has fueled security concerns for heightened country-wide election-related activities ahead of the polls for the national assembly and four provincial legislatures.
Initial investigation suggested it was a suicide attack, Lashari added.
The explosion was a suicide blast in which eight to 10 kilograms of explosives and ball bearings were used, reported Dawn. The administration in Balochistan's Quetta city has declared an emergency at all hospitals, and additional medical staff have been summoned.
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The first bomb that killed four people exploded in northwest Pakistan near the election rally of a senior politician from an Islamist party who is running for parliament from the northwestern town of Bannu.
In a video message released hours after the attack, Durrani reminisced that this was second incident targeting him.
Michael Kugelman, deputy director at Asia Program and South Asia senior associate The Wilson Center went on to tweet that both Raisani and Bilour (who had been slain earlier on Tuesday) have lost close family members to terrorist attacks previously and now they're both been martyred.
It comes amid news a plane carrying disgraced former Prime Minister Nawaz Sharif and his daughter Maryam Nawaz landed at Allama Iqbal International Airport in the eastern city of Lahore.
The law and order had suddenly deteriorated ahead of elections despite claims by the government and security forces that terrorism has been wiped out of the country.
Meanwhile, President Mamnoon Hussain and Interim Prime Minister Nasirul Mulk also condemned the attack in separate statements. Durrani is standing against cricketer-turned-politician Imran Khan, whose Pakistan Tehreek-e-Insaf party (PTI) is one of the frontrunners in the July 25 vote.
On July 7, seven people were injured when a convoy of a Muttahida Majlis-i-Amal came under attack in Bannu.