The leaders said they “welcomed the commitment by the government of the Republic of South Sudan to an immediate cessation of hostilities”.
They called on rebel leader Riek Machar to “make similar commitments”.
Recent fighting has left at least 1,000 people dead, with fierce new battles reported in oil-rich Upper Nile State.
More than 100,000 people have fled their homes in the world’s newest state, with about 60,000 seeking refuge at UN compounds across the country, according to the UN, which is sending extra peacekeepers.
There has been no confirmation from President Salva Kiir’s office that he has agreed to end hostilities.
He is engaged in a deadly power struggle with Mr Machar, his former vice-president. Members of Mr Kiir’s Dinka ethnic group and Mr Machar’s Nuer community have both been targeted in the violence.
Clashes erupted after President Kiir accused his former vice-president, who was sacked in July, of plotting a coup. The fighting quickly spread to half of Sudan’s 10 states.
East African regional leaders, who make up an eight-member bloc known as Igad, held talks in the Kenyan capital Nairobi a day after the leaders of Kenya and Ethiopia met Mr Kiir in South Sudan’s capital, Juba.
They have said they will not accept a violent overthrow of the government in South Sudan and have called on the government and rebels to meet for talks within four days.
President Kiir did not attend the talks in Nairobi nor, apparently, did any representative of Mr Machar.
Violence has continued through the week with conflicting reports on Friday about the situation in Malakal, capital of Upper Nile State.
Army spokesman Philip Aguer told Reuters news agency in Juba that the rebels in Malakal had been defeated. “[Government forces] are 100% in control of Malakal town and are pursuing the forces of the coup,” he said.
But a rebel spokesman in Unity State, Moses Ruai Lat, told AFP “the whole of Malakal” was now in the hands of Machar loyalists. “All those forces who are loyal to the president have been cleared and the former governor of Upper Nile, Simon Kun Poch, is on the run,” he said.
According to a report by regional broadcaster Radio Tamazuj, government forces drove rebel soldiers out of the town on Friday, shelling them from tanks.
Dozens of houses were destroyed in the fighting, with a tank shell killing a family of four inside one of them, while three dead bodies were found inside another, the radio said.
The government is believed to possess scores of tanks including Soviet-era T-72s.
Casualties from the fighting in the town have been “flooding” Malakal’s state hospital, the aid agency Medecins Sans Frontieres (MSF) said on Friday.
In another state, Jonglei, MSF treated gunshot victims who had walked for three days from the war-torn town of Bor in search of safe access to healthcare.
“Even prior to the latest conflict, access to healthcare was limited in South Sudan and the enormous humanitarian needs are only further exacerbated by the current crisis,” the agency added.
The fighting is affecting oil production, which accounts for 98% of government revenue.
Calling for an immediate halt to the fighting, Kenyan President Uhuru Kenyatta said two peace envoys should be appointed to talk to both sides.
He suggested that one of these could be Gen Lazaro Sumbeiywo, who helped broker the 2005 Sudan peace deal which led to the South’s independence in 2011.
China, which buys most of South Sudan’s oil, has also sent an envoy to the region to try to negotiate an end to the fighting.
The UN Security Council has voted to almost double the number of UN peacekeepers to 12,500.