The Minister said the suspension will calm the tension in the states affected by the farmer/herdsmen killings.
He said the suspension will calm the tension in the volatile states, especially in the middle belt.
Hundreds of people have been killed in Nigeria's middle belt since January when some Fulani herdsmen slaughtered people in a Benue villa.
Dan-Ali made the recommendation on Tuesday, June 5, after a security meeting with President Muhammadu Buhari at the Presidential Villa in Abuja.
"There is need to employ other channels with the affected states to reduce tension by suspending the implementation of the anti-open grazing law while also negotiating safe routes for the herders," Dan Ali said at the meeting.
"There is a need for the Nigeria police and Department of State Services to prosecute all the suspects arrested in the affected states while negotiating safe routes for the herders," the minister said.
He also recommended the launch of a Joint Task Force operation, similar to 'Operation Safe Haven' in Jos, with headquarters in Gusau, Zamfara state, to cover Zamfara and Birnin Gwari axis of Kaduna State, where incessant kidnappings and killings have also been happening.
The Inspector General of Police, Ibrahim Idris, who was also at the meeting, buttressed that a team comprising the military, police and civil defence would be deployed to Zamfara state in two weeks to secure lives and property of the people.
Others present at the meeting were the National Security Adviser, Mohammed Babagana Monguno and the Director-General of the NIA, Ahmed Abubakar.