Army spokesman Lul Ruai Koang accused the rebels of "burning civilians, maiming women and child abductions and setting ablaze properties."
Armed men loyal to former Vice President Riek Machar killed 11 government soldiers and 28 civilians from Saturday to Thursday, Koang said in a press statement. Twenty-one rebels were also killed, he said.
A spokesman for the rebels was not immediately available for comment.
South Sudan, the world's youngest nation, sank into civil war in 2013 after President Salva Kiir, an ethnic Dinka, sacked Machar, a Nuer, from his position as vice president. Subsequent fighting often followed ethnic lines and human rights groups say both sides targeted civilians.
A peace pact in 2015 ostensibly ended the fighting but has frequently been violated. Major clashes broke out again in July. Machar fled the country and is seeking medical treatment in South Africa. He has been replaced as vice president by General Taban Deng Gai.
The government wants the international community to designate the rebels as terrorists and take punitive measures against them.
Koang said that could include "travel bans, asset freeze and extradition to ICC of key players including ... Riek Machar." The Hague-based International Criminal Court (ICC) tries suspects accused of war crimes and genocide.
On Monday, the United Nations Mission in South Sudan (UNMISS) said it had received reports of horrific attacks on civilians, including some who were burned to death, and urged both sides to control their forces.