"We heard his slander the other day, lying, blatantly lying," Burhan said in a speech at a military graduation on Friday, Reuters reported.
"If you overstep your mandate, we will put you out of Sudan."
The comments come days after UN representative Volker Perthes gave an update to the Security Council on efforts in Sudan, where he commented on the country's economic turmoil, violence against protesters and priorities for a transition to elections.
Perthes' mission has involved holding a series of consultations, along with the African Union, aiming at coming to a political solution following a military takeover in October which ended a power-sharing arrangement with civilian parties.
"We say to him you have a specific mandate, and we said we are open for you to sit in talks, but for you to lie and to try to manage the Sudanese people, we will kick you out," said Burhan, who led the coup.