Mr. Machar has said that the 11 senior politicians held as suspected plotters have to be released before there can be a cease-fire. Mr. Kiir has said they must be tried for their conspiracy to overthrow the government and cannot be freed summarily.

“The United States strongly believes that the political prisoners currently being held in Juba must be released,” Ms. Thomas-Greenfield said. “And each day that the conflict continues, the risk of an all-out civil war grows as ethnic tensions and more civilians are killed, injured or forced to flee.”

She added that the humanitarian situation had worsened with every passing day. More than 200,000 people have been displaced inside South Sudan, including about 60,000 taking shelter at United Nations compounds. More than 30,000 refugees have fled to neighboring countries like Uganda, Kenya, Ethiopia and Sudan.

Thursday was the ninth anniversary of the Comprehensive Peace Agreement that created the framework for South Sudan’s independence from Sudan. It was also the third anniversary of the referendum in which an overwhelming number of people officially voted to split off and create their own nation, South Sudan.

Now, the conflict is nearing the one-month mark, with neither side prepared to give ground in negotiations or on the battlefield. Col. Philip Aguer, a spokesman for the South Sudanese military, said that there had been fighting on Thursday near Bentiu, the capital of the oil-producing Unity State.

In Bor, the government’s military, the Sudan People’s Liberation Army, “is fighting a huge number of armed civilians together with the forces that defected from the army some weeks ago with all their equipment,” Colonel Aguer said.

The World Health Organization had no figures on overall fatalities in the conflict, but it had documented 2,566 cases of gunshot wounds as of Wednesday, spread across six of South Sudan’s 10 states. Displaced people have described both indiscriminate killing of civilians as well as targeted attacks against ethnic groups.