The investigative body is seeking approval from the Judiciary to confiscate the mobile phones of the arrested individuals including Okiya Omtatah.
Murkomen had earlier denied state involvement in the abductions.
KNBS made the remarks in the latest report.
The National Land Commission has issued a 15-day notice.
Nyariki's remains were found in the main suspect's car on December 20.
The British woman was in the country with her family for holiday and philanthropic activities.
The latest ruling came after a petition was filed on December 26.
Okiya Omtatah was arrested among other protestors on Monday, December 30.