New south Sudanese leader Salva Kiir has appealed for calm following the death of predecessor John Garang.
The clashes are some of the worst in Khartoum for years
A second day of unrest in Sudan's capital, Khartoum, brought the death toll to 46, police said.
Mr Kiir told the BBC he would work with the government to ensure the country's peace process continues.
"I am confident that the peace agreement will hold because there is nothing that will derail it. Nobody wants war," he said.
Garang signed a deal to end 21 years of civil war in January and was sworn in as vice-president of Sudan three weeks ago.
Mr Kiir has been chosen as new leader of the former southern rebel group, the Sudan People's Liberation Movement (SPLM), and is expected also to take the post of vice-president.
News of Mr Garang's death sparked riots on the streets of the capital, Khartoum, on Monday leading to dozens of deaths, before security was restored.
But while central Khartoum remained relatively quiet on Tuesday, clashes erupted on the outskirts of the city between northerners - mainly Arabs - and southerners.
There was no confirmation of casualties in the latest violence though the BBC's Jonah Fisher in the capital said there were stories of gunshots in some areas.
William Ezekiel, managing editor of the Khartoum Monitor newspaper, said Tuesday's violence was largely sparked by northerners, in revenge attacks for Monday's clashes.
A UN official in Khartoum said angry southerners had converged on Arab areas and had killed a Muslim imam.
"The situation is turning religious and that will be even more dangerous," he told the Associated Press agency.
Mr Garang will be buried in the main southern town of Juba on Saturday after being killed in a helicopter crash over the weekend.
In New Site, a southern Sudanese settlement near the scene of the crash, former rebel fighters and civilian supporters gathered to pay their respects.
His body was placed in a wooden coffin covered with a flag.
It will be taken to other key towns in southern Sudan to allow supporters to pay final respects before the state funeral in Juba, a spokesman announced.
Meanwhile, US President George W Bush has dispatched two envoys to Sudan to try to reinforce the peace process.
Tensions are still high as Sudan continues to take in what Garang's death means for the country's fragile peace, our correspondent says.
On Tuesday, the United Nations Security Council urged calm. "This is a time for the world community to come together to support Dr Garang's vision of a united and peaceful Sudan," it said.
In choosing Mr Kiir, the SPLM has sent a clear signal that the group remains committed to Mr Garang's policy of integration with the north, our correspondent says.
After working so long under Garang, Mr Kiir has been handed his most difficult task - holding together, then delivering on, Sudan's hard-won peace, he says.