The bodies were found in Bentiu: one grave with 14 bodies and a site nearby with 20 bodies, said UN human rights office spokeswoman Ravina Shamdasani.
The government minister of information Michael Makuei Lueth said Bentiu is under the control of rebels loyal to the country's former vice president, Riek Machar, indicating they were responsible for the killings.
US Secretary of State John Kerry spoke on the phone today with Machar, who said he told Kerry he is ready for talks with Kiir, likely to take place in Ethiopia.
"I will form a high-level delegation, to which I will give full power to negotiate an accord," Machar told Radio France Internationale.
"We want Salva Kiir to quit power. We want a democratic nation and free and fair elections."
Some 20,000 people seeking safety have crowded round the UN base in Juba, the capital, where at least two other mass graves are reported to have been found, UN human rights chief Navi Pillay said.
The UN Security Council is expected to vote later today on a resolution to increase the number of UN troops in South Sudan from 7,000 to 12,500 following a call by Secretary-General Ban Ki-moon for more UN force.
UN staff visited the mass grave in Bentiu yesterday. Originally the UN said 75 bodies had been seen but later corrected that statement to 34 bodies seen and 75 people missing and feared dead.
Officials say Kiir and Machar have agreed to meet but specifics including the status of Machar's imprisoned compatriots are holding up talks.
South Sudanese troops, meanwhile, are advancing on Bor in order to take it back from troops loyal to Machar, said military spokesman Colonel Philip Aguer.
The military said armed elements have entered a UN refugee camp in Bor, a frightening situation for the 17,000 civilians seeking refuge there. Government troops will also soon advance on Bentiu, in oil-rich Unity state, he said.
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