SSP Dharmendra Yadav said a case will be registered against the family only if the charge that the meat found in Akhlaq's home was beef was found to be true.
"It's a very sensitive matter. The Circle Officer, Dadri, will head a probe into the charges," he said.
After the meeting with Yadav, Sanjay Rana, father of Vishal Rana, an accused in the 2015 lynching case threatened that a maha panchayat will be held in the village tomorrow as police have failed to register an FIR against Akhlaq's family.
"The villagers have decided to hold a maha panchayat tomorrow as police have failed to register an FIR based on our complaint. Residents of Satha Chaurasi village will also attend it," he claimed.
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He claimed that an eight-member delegation from the village had yesterday met Union Home Minister Rajnath Singh, who assured he would speak to the Uttar Pradesh government in this regard.
Chief Minister Akhilesh Yadav had earlier this week questioned the authenticity of the forensic report and said "there was nothing objectionable in his house. Every eye is on this matter. Everyone wants that the victim's family should get justice as murder had taken place."
VHP activists had also staged a protest at the Collectorate demanding that the FIR be registered against Akhlaq's family and the financial help given to them be withdrawn.
Meanwhile, more police personnel have been deployed in the village.