The bombings, minutes apart, hit a crowded market in the Shiite-dominated city.
At least 11 bodies were taken to hospital, along with 19 wounded people, said Wasim Baig, a spokesman for the Civil Hospital in Quetta.
Basir Khan Wazir, the top government official in Parachinar later told AFP that apparently both the blasts were carried out by two suicide bombers.
Condemning the terrorist attacks in Parachinar and Quetta, PM Nawaz directed concerned authorities to increase security across the country."Terrorists are attacking soft targets and no Muslim can ever imagine to commit such horrific act", Sharif said.
At least 30 people have been killed and 100 others injured in Parachinar, Dawn news reported.
He also expressed his solidarity with the people and government of Pakistan and its efforts in fighting terrorism and violent extremism.
Kurram is one of Pakistan's seven semi-autonomous tribal districts which are governed according to local laws and customs.
Media reports said that it was a suicide attack, when a suicide bomber blew himself at Toori market, a busiest shopping site of the area.
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Jamaat-ul-Ahrar, a splinter group of the Pakistani Taliban, claimed responsibility for the attack.
There was no immediate explanation for the dual claims. A breakaway Taliban faction later claimed responsibility for the attack.
Four policemen were among the dead, while three others remain in critical condition, he said.
At the hospital in Quetta, anxious children stood by the bloodstained cots of wounded relatives, and Pakistani soldiers visited injured colleagues.
Later on Friday evening, two armed men on a motorcycled opened fire on security personnel in Karachi, killing four - an assistant sub-inspector was among those killed.
According to Police surgeon Ali Mardan nine people, including three police officers and one traffic warden, were killed in the blast.
He vowed more such attacks.
Video footage after the attack showed civilians dragging bleeding victims outside to waiting ambulances in the chaos that came when the bombs exploded before the sundown meal breaking the daily Ramadan fast.
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