PHOTO: AFP
The Taliban have not officially commented, but an unofficial statement circulating among Taliban fighters on WhatsApp and seen by AFP confirmed the claim.
The blast comes at a delicate moment as a deal between the insurgents and Washington to end America's war in Afghanistan is believed to be imminent.
Balochistan IGP Mohsin Hassan Butt said the explosion -- the latest violence in a string of attacks in the province -- was caused by a remotely detonated bomb in Kuchlak.
"The death toll is four ... and there are 23 others wounded," senior police official Abdul Razzaq Cheema told AFP.
A senior official with the Balochistan government confirmed that Ahmadullah Azkhundzada, brother of the Taliban chief Haibatullah Akhundzada, was among the dead.
"This is confirmed that he is the brother of Haibatullah," he told AFP on condition of anonymity as he was not authorised to speak to media.
Four worshippers martyred in blast inside mosque in Quetta suburbs
Two Taliban sources -- one in Quetta, and one in Chaman also said Ahmadullah had been killed.
"The explosion took place while Hafiz Ahmadullah was reading sermon. Hafiz Ahmadullah was killed," one said.
The list of dead and wounded issued by Sandeman Hospital also carries the name "Hamdullah son of Maulvi Mohammad Khan".
Taliban expert Rahimullah Yusufzai said the mosque was attached to a madrassa that had formerly been run by Haibatullah, the Taliban leader.
"After he became the emir he left this place," Yusufzai told AFP.
"His younger brother ... was running the madrassas. He has been killed as far as we know."
Local residents in Kuchlak on condition of anonymity also said the mosque belonged to the family.
They said that Ahamdullah was a respected Islamic scholar but had no links with the Taliban, taking over only after Haibatullah left to head up the Taliban in 2016.
The police official Cheema denied the mosque was owned by the family, telling AFP that it instead belonged to a local Baloch man who was out of town at the time.
There was no immediate claim of responsibility for the attack, which came as speculation has reached fever pitch in Kabul that an announcement about a deal between the US and the Taliban is imminent.
The foes have been negotiating in Doha over the past year for a pact that would see the Pentagon begin to withdraw its 14,000 troops from Afghanistan.
Tweets from the Taliban and Zalmay Khalilzad -- the US special envoy leading the talks -- suggest work still remains to be done.
Pakistani foreign minister Shah Mehmood Qureshi said Friday that Prime Minister Imran Khan had spoken with President Donald Trump about the Taliban talks, adding that Pakistan remains committed to the process.
Washington is keen to end its 18-year involvement in Afghanistan, where it has spent more than $1 trillion, and President Donald Trump has said he wants troops out.
In return, the Taliban would commit to various security guarantees, including that the hardliners would not allow Afghanistan to become an extremist safe haven.
A US-Taliban agreement would not alone bring peace to Afghanistan, as the insurgents still need to reach an agreement with the government in Kabul, whom they dismiss as puppets
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