It was difficult to ascertain which side started the fighting, presidential spokesman Ateny Wek Ateny told dpa.
Kiir signed the agreement on Wednesday, but also expressed reservations about the deal, which aims to end a 20-month military conflict. It had been approved by rebel leader Riek Machar the week before.
Machar's spokesman Dickson Gatluak said his troops were on the 'defensive' against the government, suggesting the army initiated the latest round of violence. Infantry forces attacked rebel forces with heavy machineguns and gunboats in various locations of Unity State, according to Gatluak.