More than 180,000 people have been displaced in the conflict. Aid workers say many are living without shelter, clean water and sanitation.
Tensions are increasing around the rebel-held cities of Bor, in Jonglei state, and Bentiu, in the northern state of Unity.
A build-up of military personnel around both cities has prompted fears that renewed heavy fighting may be imminent as the government attempts to regain control, the BBC's Alastair Leithead reports from the capital, Juba.
One rebel spokesman told Reuters its troops were marching towards Juba, while a spokesman for the government said its forces were closing in to recapture Bor.
Delegates from both sides began arriving in the Ethiopian capital on Wednesday but talks were delayed until the full negotiating teams had arrived.
The BBC's Emmanuel Igunza in Addis Ababa says the rival teams are in the same hotel but are currently in talks only with mediators.
The mediators are preparing the ground for direct talks, he adds.
Observers have said the discussions are likely to be complicated, as the two sides will have to agree on a mechanism to monitor any ceasefire.
Meanwhile, the US state department said it had ordered a "further drawdown" of its embassy staff in Juba "because of the deteriorating security situation".
It evacuated a large number of non-essential staff soon after the fighting began on 15 December.
But ambassador Susan Page told Reuters: "We are not suspending our operations. We are just minimising our presence."
However, the state department also said that, from Saturday, it would no longer be providing consular services to US citizens in South Sudan.
And it repeated its advice to its citizens to leave the country, announcing a further evacuation flight from Juba "to the nearest safe haven country" on Friday.
The United Nations, however, is flying more staff into Juba to help in the aid effort and to protect civilians' human rights. One official said US staff working for the UN had not been asked to leave.
South Sudan is the world's newest state. It was formed in 2011, gaining independence from Sudan after decades of conflict.
The latest trouble has its roots in tensions that go back long before 2011, rebels were fighting each other as well as for independence.
But what began as a squabble between former fighters turned politicians has taken on an ethnic dimension.
Politicians' political bases are often ethnic. President Kiir is from the Dinka community while Mr Machar is a Nuer.
Mr Kiir has ruled out any power-sharing arrangement with his rival in the longer term.