War-torn South Sudan faces a catastrophic "tipping point" amid famine and genocide warnings, an aid agency has stated, as the conflict entered its fifth month with no sign of the bloodshed ending.

"We either act now or millions will pay the price," Oxfam chief executive Mark Goldring said on Thursday.

"We face a mammoth task of getting massive levels of aid to people at the worst time of the year, when rains make many areas hard to reach and turn roads into rivers of mud," Goldring said in a statement.

"We need a massive and rapid global surge in aid to prevent catastrophic levels of hunger. We cannot afford to wait, we cannot afford to fail."

President Salva Kiir and rebel chief Riek Machar signed a fresh ceasefire agreement last week but fighting broke out hours later, the second time in the five-month conflict that a truce has failed to hold.

More than a third of South Sudan's population - 3.7 million people - are facing emergency and crisis levels of hunger. In the war-torn Unity state, the key oil producing region, more than three-quarters need aid, according to the UN.

The ceasefire agreement, signed last week in the Ethiopian capital Addis Ababa, was the result of weeks of mounting international pressure and shuttle diplomacy. But fighters on the ground appear to have paid little notice to it.

'Precursors of genocide'

The war in the world's youngest nation has claimed thousands of lives, with more than 1.2 million people forced to flee their homes, AFP news agency reported.

The conflict, which started as a personal rivalry between Kiir and Machar, has seen the army and communities divide along ethnic lines, pitting members of Kiir's Dinka tribe against Machar's Nuer.

UN rights chief Navi Pillay, a former head of the UN genocide court for Rwanda, has said she recognised "many of the precursors of genocide" listed in a report on atrocities released last week by the organisation.

UN Secretary General Ban Ki-moon this week warned half of the country's population will suffer if war continues.

"If the conflict continues, half of South Sudan's 12 million people will either be displaced internally, refugees abroad, starving or dead by the year's end," Ban said.

The UN's $1.27bn funding appeal is only 40 percent funded, with a shortfall of over $700 million.

The United Nations food agency has warned there is only a "small window of opportunity" to avert famine and appealed for relief agencies, who have been subjected to armed attacks and looting, to be allowed unfettered access.

The war erupted on December 15 when Kiir accused Machar of attempting a coup. 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.

Despite pressure to end fighting, many fear that political leaders can no longer hold back their warring forces as communities spiral into cycles of revenge attacks.

An Amnesty International report last week described civilians including children executed by the side of the road "like sheep", gang rapes of women using sticks, and other victims "grotesquely mutilated" with their lips sliced off.