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It is not clear exactly what the circumstances were around the death of Samira Sindhu, 28.
A man was reported to have shot her because she would not stand up while singing, but he has said he shot her by accident while firing in the air.
She was eight months pregnant.
It happened at a circumcision celebration in a village called Kanga, near Larkana city in Sindh province.
The singer's husband, Ashiq Sammoo, said in a police complaint that a man at the celebration had pointed a gun at his wife and "threateningly ordered her to stand up and sing". When she said she was pregnant and could not stand, he said, the man shot her.
One man has been arrested in connection with the death. Tariq Jatoi told journalists outside court that he had fired in the air in celebration and a bullet hit the singer by mistake. He was remanded in custody.
Protesters have demanded that two men who were also present at the scene should be arrested as well.
A video circulated on social media does not clearly show anyone threatening Ms Sindhu. It shows her sitting on a stage, accompanied by musicians, singing, when three men approach the stage and shower her with banknotes as is customary. She stands and keeps singing. Just as the men exit the frame, three shots are heard, and she falls.
Ms Sindhu was a locally known singer. She had produced at least eight albums of Sindhi folk and Sufi music but her main source of livelihood was to sing at family functions, as is the case for many musicians across Pakistan.
Results of her post-mortem examination and of a blood alcohol test on Mr Jatoi are expected to be examined in court. Drinking alcohol is prohibited for Muslims in Pakistan.