In two separate posts on their purported Facebook pages, Bishnoi and Brar took responsibility for the murder of the Punjabi singer.
Mint has not been able to independently confirm their authenticity.
Moosewala was shot dead by unidentified assailants in Punjab's Mansa district, a day after the state government withdrew his security cover.
Deputy Superintendent of Police (Mansa) Gobinder Singh told PTI that several bullets hit Moosewala, 27, who was travelling along with his two friends in a jeep when he was attacked at village Jawahar Ke.
Mansa civil surgeon Ranjeet Rai told reporters that Moosewala was brought dead at the civil hospital. He said that the two others who also sustained bullet injuries have been referred to another hospital.
He had fought on the Congress ticket from Mansa assembly seat in the recent assembly election and was defeated by AAP's Vijay Singla.
Shubhdeep Singh Sidhu, known as Sidhu Moosewala, was among the 424 people whose security was withdrawn by the Punjab Police on Saturday.
Leaders of the Congress and other political parties expressed shock and anger over the killing of Moosewala and attacked the AAP government for withdrawing his security cover.
Chief Minister Bhagwant Mann said no one involved in the gruesome murder will be spared and appealed for calm.
“I am shocked and deeply saddened by the gruesome murder of Siddhu Moosewala. Nobody involved will be spared. My thoughts and prayers are with his family and his fans across the world. I appeal everyone to stay calm," said Mann in a tweet.
Punjab Congress chief Amrinder Singh Raja Warring, who played a major role in bringing Moosewala into the Congress fold, said he was "shocked beyond belief and expression" and demanded dismissal of the Aam Aadmi Party (AAP) government.
''He was showered with bullets in Mansa just 2 days after @BhagwantMann govt withdrew his security. @AAPPunjab govt has lost moral authority. It must be dismissed," said Warring in a tweet.
BJP leader Manjinder Singh Sirsa, who had earlier questioned the state government after the names of the people whose security was withdrawn became public, too demanded action against Chief Minister Bhagwant Mann and AAP chief Arvind Kejriwal.
"We have been warning Punjab Govt to pay attention to Punjab’s situation. I demand an FIR against Bhagwant Mann for negligence of his Chief Ministerial duties which has cost the life of #sidhumoosewala. Bhagwant Mann along with @ArvindKejriwal should be booked u/s 302,'' he said.
Former chief minister Amarinder Singh alleged that law and order has completely collapsed in Punjab.
''Criminals have no fear of law. AAP Punjab government has miserably failed. Nobody is safe in Punjab!
The others whose security has been removed included former MLAs, two Jathedars of Takht Damdama Sahib and Takht Kesgarh Sahib, heads of Deras and serving and retired policemen.
Moosewala had joined the Congress last year ahead of the Punjab assembly polls.
The singer had faced criticism from several quarters for promoting gun culture in his songs. He had also been booked for allegedly promoting violence through his song ''Sanju''.
He was booked under the Arms Act and the Disaster Management Act in Barnala after photographs showing him firing an AK-47 rifle at a firing range during the COVID-19 lockdown appeared on social media.
