Local official Nasrullah Khan told AFP that the first blast detonated as the market was crowded with shoppers preparing for the Eid ul-Fitr festival marking the end of Ramadan.
"When people rushed to the site... to rescue the wounded, a second blast took place," he said, adding that he could not give further details of the attack but that officials fear the toll will increase.
Sabir Hussain, the medical superintendent at Parachinar's main hospital, said it had received 13 bodies and 124 wounded.
Pakistan Prime Minister Nawaz Sharif called for security to be increased across the country as he condemned the attack, saying that no Muslim could ever imagine committing such a "horrific" act.
Pakistan has seen a dramatic improvement in security in the last two years, but groups such as the umbrella Pakistani Taliban and other outfits still retain the ability to carry out attacks.
Local lawmaker Sajid Hussain Turi, the owner of the market, said bazaars in Parachinar had been barricaded off and vehicles banned from the area after multiple attacks have hit the city this year.
Parachinar was the location of the first major militant attack in Pakistan in 2017, a bomb in a market which killed 24 people in January and was claimed by the Pakistani Taliban. In March, a second Taliban attack killed a further 22 people.
There was no immediate claim in Friday's attack.
Kurram, one of Pakistan's seven semi-autonomous tribal districts, is known for sectarian clashes between Sunnis and Shiites, who make up roughly 20 per cent of Pakistan's population of 200 million.
The twin blasts in Parachinar followed a bombing earlier in the day in southwestern Quetta, capital of the insurgency-wracked Balochistan province, which killed at least 13 people.
Investigators said the attack targeted police. It was claimed by both the local affiliate of ISIS and by Jamaat-ul-Ahrar (JuA), an offshoot of the Pakistani Taliban, according to the SITE monitoring group.
There was no immediate explanation for the dual claims. ISIS-Khorasan Province, the Middle Eastern group's affiliate in Afghanistan and Pakistan, has been known to work with the myriad of Pakistani terrorist groups in previous attacks, including with JuA.
Officials at the city's Civil Hospital said at least 13 people were killed and around 20 injured, mostly by shrapnel. Police officials said nine policemen were among the dead.
At the hospital in Quetta, worried children stood by the bloodstained cots of wounded relatives, and Pakistani soldiers visited injured colleagues.
Stunned survivors could give few details about the attack. "I was sitting on a chair. There was an explosion. I got injured and fell down," said one victim, Gulzar Ahmad.
Pakistan has waged a long war with militancy, but security has markedly improved in the country since its deadliest-ever terror attack, an assault on a school in northwestern Peshawar in which Taliban gunmen left more than 150 people dead, most of them children.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.