Security forces had restored calm in central Khartoum, but the situation was tense elsewhere, as some supporters of former rebel leader John Garang blamed his death in a helicopter crash on the government.
The government and Garang's own Sudan People's Liberation Movement said his death was an accident and dismissed talk of a plot as they sought to keep alive the fragile north-south peace deal Garang championed.
On Monday, President Bush said the United States remained committed to the peace process in Sudan and urged its people to refrain from violence, describing Garang as a "visionary leader and peacemaker."
Two senior State Department officials were heading for Sudan to tell leaders in Khartoum and southern Sudan the peace process must proceed.
Garang and 13 other people died Saturday when a helicopter crashed into a mountain in southern Sudan in bad weather.
A Western diplomat in Khartoum, speaking on condition of anonymity because of the sensitivity of the security situation, said Sudanese police appeared to have regained control in the capital but that the atmosphere remained tense.
"The streets are calmer but still explosive," said the diplomat. "There was so much damage and so many killings and looting and it is possible there will be reactions against that."
On the outskirts of Khartoum on Tuesday, hundreds of soldiers monitored streets and residents wielded large, club-like sticks to protect themselves.
On Monday, grief-stricken supporters of Garang rampaged in Khartoum, smashing car windows, setting fires, looting shops and in some cases chasing pedestrians away with stones.
The government reported that 36 people were killed and about 300 were injured in
Garang, from southern Sudan, became the country's first vice president last month as part of the US-backed peace deal that ended a two-decade-long civil war between his rebel force and the army of Sudan's Islamic-oriented government based in Khartoum.
The charismatic Garang was hailed for helping seal the peace deal, particularly across southern Sudan and among the several million southern refugees living in Khartoum, many of whom took part in Monday's violence.
Three days of national mourning were declared following his death, but it was not immediately clear when or where his funeral will be held. SPLM leaders are meeting in southern Sudan and are expected to make an announcement soon.
An overnight curfew was lifted at 6 a.m. Tuesday. The skeletons of burned cars had been towed away, leaving charred ashes and broken glass scattered over streets. Some Khartoum residents were still cautious and a number of downtown business remained shuttered and traffic was lighter than normal.
The SPLM named Garang's longtime deputy, Salva Kiir Mayardit, to succeed him as head of the movement and president of south Sudan. Kiir will also likely be Sudan's first vice president, according to the January peace agreement that says the SPLM leader will hold that position, said Kenyan Gen. Lazaro Sumbeiywo, a mediator in the peace talks.
Garang was the dominant voice of the south since 1983. A colonel in Sudan's army, he was sent south to quell a rebellion but deserted to form a rebel movement that fought the Muslim government in Khartoum for a share of wealth and political power for the mostly Christian and animist south. More than 2 million people died in the conflict.
The deal and Garang's ascension to the national unity government were signs of hope for others who feel marginalized in Sudan. Many in the east and west, including in Darfur, who are fighting their own battles with Khartoum, considered Garang an advocate.
(Associated Press writer Mohamed Osman contributed to this report from Khartoum.)