According to the police, Mr Parray, his two brothers and father were at his aunt Hubba Begum's home when two terrorists barged in, asking for his identity card. The 28-year-old constable, who joined the BSF seven years ago, fought the intruders, injuring one of them. However, his aunt was also injured.
Mr Parray rushed home to change so he could take her to the hospital, police said. According to eyewitness accounts, four terrorists entered Mr Parray's single-storey home and cornered him. His father and brothers pleaded with the attackers to spare his life, but Mr Parray was shot twice from point-blank range - in his head and abdomen.
According to senior police officer S P Vaid, the attack was carried out by the terror outfit Lashkar-e-Taiba.
On Tuesday night, police had launched a cordon operation in the constable's neighbourhood, Parray mohalla, and it is reported that terrorists believed he was involved in the exercise. Mr Vaid, however, denied this report.
"This is absolutely baseless as terrorists have no excuse for the senseless and brutal killing," he said.
Constable Parray had come home to oversee the renovation of his house and look for better job prospects for his brothers, who are daily wage workers. His brothers told the police that Constable Parray was planning to set up a shop for them.
"The family has lost their lone bread earner," said his uncle Mohammed Maqbool Parray. "Rameez was the only one with a stable income."
On Thursday, senior BSF, Central Reserve Police Force, Police and Army officers laid wreaths on Constable Parray's body before it was handed over to the family. The family took the body in an ambulance for burial. Fearing terrorists, they did not want any police presence.