Ranjan's 75-year-old father Radha Chaudhary demanded a CBI investigation in the murder saying he has no faith in local police.
The family wants a CBI probe so that the culprits could be brought to justice, said Radha Chaudhary's another son Gautam.
Ranjan's wife said there could be political reason behind his murder.
"There is indeed a political angle to my husband's murder two days ago as he did not have personal enmity with anyone. But there could also be professional reasons," Ranjan's wife Asha Devi said.
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Gautam urged the state government to bear the cost of education and related needs of Ranjan's children.
"The state government should bear the cost of education and related needs of 16-year-old Ashish Ranjan and his eight year-old sister Sakshi Ranjan as his father will no more be with them to secure their future," Gautam Ranjan told PTI.
The district bureau chief of vernacular daily 'Hindustan', Ranjan was shot dead by unidentified assailants near a fruit market on Station Road here on May 13.
that he was targeted by incarcerated RJD leader Md. Shahabuddin's men, and Bihar Police lacked will to conduct a free, fair and impartial probe in the matter.
Under the circumstances, the murder case should be handed over to CBI, he told reporters and demanded security to Ranjan's family and a compensation of Rs 25 lakh to his kin.
The BJP MP from Siwan, Om Prakash Yadav, met the grieving family and offered financial assistance to them.
An RLSP delegation comprising its two MLAs Sudhanshu Shekhar and Lalan Paswan also met Ranjan's family.
Meanwhile, mediapersons under the auspices of Bihar Working Journalists Union (BWJU) condemned Ranjan's murder and demanded security to journalists throughout the state.
"The incident had put all journalists at risk in discharging their duties for fair and fearless reporting on any issue," the BWJU said.
"Bihar government should ensure safety and security of journalists to enable them discharge their duties without fear," it said.
The BWJU also demanded that Bihar government provide Rs 25 lakh assistance to the kin of the slain journalist and also regularisation of service of his wife, who is a contractual teacher. It said arrangement should also be made by the state government to ensure free education for Ranjan's children.