The allegation of the lower legislative chamber came after its defense committee met with the security chiefs in Abuja on Wednesday.
The speaker also promised to give whatever legislative support the security chiefs will need to nip insecurity bedeviling the nation in the bud.
The Peoples Democratic Party (PDP) lawmaker was the first to tender his contribution during the motion.
The mace-snatching incident is one of the several attempts by the APC to indirectly oust the top lawmaker from his position but the move met brick walls.
Mr Lawan who gave his own side of the story described the report as misrepresentation of facts.
The request is coming a month to the scheduled date for the governorship election wherein the state governor, Yahaya Bello, is seeking another term in office.
Mr Buhari made the presentation on Tuesday at a joint session of National Assembly members.
Mr Buhari made the presentation of the appropriation bill to the joint session of the lawmaking arm of government on Tuesday.
He is representing Yorro state constituency.
Mr Lawan has also promised early passage of the budget if submitted early to lawmakers.