According to al-Ahd news website, al-Zalfawi has praised his relative for the suicide bombing and said more such operations are on the way.
On Friday, 21 Shia worshippers lost their lives and scores of others were injured in the terrorist attack on Imam Ali (AS) mosque, in the village of Qadih, in Qatif region.
The ISIL terrorist group has claimed responsibility for the blast.
Suadi King Salman bin Abdul Aziz has pledged to punish all of those behind the terrorist attack on Imam Ali (AS) Mosque and to combat terrorist ideologies.
But Shias in Qatif region are not convinced, saying that anti-Shia propaganda and Takfiri rhetoric that is common in Saudi media give rise to terrorist attacks against Shias.
Meanwhile tension is running high in Saudi Arabia’s Eastern province following the deadly bomb attack.
The residents of the al-Qadeeh town in Qatif, where the attack took place, have voiced their anger at the Saudi government’s lack of care for their safety.