At some point after Idi Amin took power in Uganda in 1971, Kamuntu became part of the exile-based Save Uganda Movement, a militant group attempting to overthrow Amin. Kamuntu lectured at Nairobi University in 1978. He lectured in Makerere University's Faculty of Commerce before it was shifted to the current Makerere University Business School in Nakawa. From 1992 until 1995, Kamuntu served as the chairman and managing director of Nile Bank Limited, a private commercial bank in Uganda. Between 1995 and 1997, he worked as a private consultant. From 1997 until 2001, he served as the National Coordinator for the Private Sector Development Program of the Ugandan Government. He entered politics in 2001, contesting for the parliamentary seat of Sheema County South, Bushenyi District. He was elected and was re-elected in 2006.