Independent witnesses said fighting broke out by dawn Sunday around Bentiu - the Unity state capital which has changed hands several times in recent weeks - but that was impossible to say which side fired first.
The rebels said government troops also attacked in neighbouring Upper Nile State, and that they reserved "the right to fight in self-defence".
But South Sudan's defence minister, Kuol Manyang, told AFP that it was the rebels who attacked first in Bentiu and that the opposition suffered heavy casualties.
"They attacked first thing this morning. They attacked our position and 27 of them were killed. They have a policy of attacking then going to the media," he said.
Mr Kiir also insisted he wanted peace, telling a crowd in Juba that "we have ordered our forces not to lift a foot from where they are to attack rebels". He said, however, that Mr Machar only signed the deal "under pressure".
The two sides had agreed to a ceasefire in January, but that deal quickly fell apart and unleashed a new round of fierce fighting.
Observers have said both side will face challenges in implementing a truce, with the rebels made up of a loose coalition of army defectors, ethnic rebels and, allegedly, mercenaries from Sudan. On the government side, the command structure under Mr Kiir is also seen as weak.
The peace deal signed on Friday came after massive international pressure on both sides to stop a war marked by widespread human rights abuses, a major humanitarian crisis and fears the world's youngest nation was on the brink of a genocide and Africa's worst famine since the 1980s.
The war in the world's youngest nation has claimed thousands - and possibly tens of thousands - of lives, with more than 1.2 million people forced to flee their homes.
The conflict, which started as a personal rivalry between Mr Kiir and Mr Machar, has seen the army and communities divide along ethnic lines, pitting members of Mr Kiir's Dinka tribe against Mr Machar's Nuer.
UN rights chief Navi Pillay, a former head of the UN genocide court for Rwanda, said she recognised "many of the precursors of genocide" listed in a UN report on atrocities that was released during the week.
These included broadcasts urging rape and "attacks on civilians in hospitals, churches and mosques, even attacks on people sheltering in UN compounds - all on the basis of the victims' ethnicity".
Testimonies in a report this week by Amnesty International describe civilians, including children, executed by the side of the road "like sheep" and other victims "grotesquely mutilated" with their lips sliced off.
The war erupted on December 15 with Mr Kiir accusing Mr Machar of attempting a coup. Mr Machar then fled to the bush to launch a rebellion, insisting that the president had attempted to carry out a bloody purge of his rivals.
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