A TTP statement on Wednesday also confirmed that talks were underway in Kabul and that a ceasefire has been put in place will May 30.
The Balochistan Liberation Army (BLA) separatist group has warned of more attacks to come.
Both Ankara and Riyadh have faced tensions with the US and some Western countries in recent years.
Pakistan and Afghanistan continue to be unstable which could harm the wider region.
A separatist group, the Baloch Liberation Army (BLA) based in southwestern Balochistan province bordering Afghanistan and Iran, claimed responsibility for the blast.
Ilhan Omar went on an apparently unofficial trip to Pakistan where she met with a number of officials including ousted PM Imran Khan.
The overall context is that Iran has a continued interest in the outcome of political changes in Afghanistan. It also sees this as part of a wider struggle in Central Asia.
Islamists stepped up attacks on Pakistani security forces as Kabul accused Pakistan of bombing a refugee camp, killing 47 civilians.
But Khan's party also submitted papers nominating the former foreign minister as a candidate.
Opposition parties were able to secure 174 votes in the 342-member house, in support of the no-confidence motion, the house speaker said.