Heavily-armed police and soldiers are on patrol in the Sudanese capital, Khartoum, after 130 people were killed in three days of violence.
Salva Kiir said he was confident the peace deal would hold
An overnight curfew seems to have been respected, with no more of the clashes between southerners and Arabs sparked by southern leader John Garang's death.
In south Sudan, people are preparing to pay their respects as Mr Garang's body is to be taken around the main towns.
He died three weeks after being named vice-president as part of a peace deal.
A Sudanese minister has also urged Muslim preachers not to further inflame tensions - most northerners are Muslims, while southerners are generally Christians or animists.
"This directive is to the imams of mosques: You must prevent discord - if that is what it is you're doing - You must prevent this by preaching that which unites people and that which brings people closer," said Religious Affairs Minister Kamal Sid-Ahmad.
The US has expressed deep concern over the situation. Its two envoys are due to meet President Omar al-Bashir.
Most of the violence has occurred in the capital, Khartoum, where some 400 people have been injured , according to the Red Cross.
State media said more than 1,400 suspects have been arrested.
The city centre lies in ruins, with shops burnt and looted and cars wrecked, Reuters news agency reports.
A curfew was in place in Khartoum overnight for a third night running and appeared to pass off calmly, the BBC's Jonah Fisher says.
He says three days of rioting have seen the level of violence ebb and flow, but there are now hopes that the worst may have passed.
At least 19 people are reported to have been killed in the southern town of Juba, where Mr Garang is due to be buried on Saturday and in Malakal.
Northerners - many of whom have lived in the south for decades - are said to be packing up and leaving the city.
Leaders of both sides earlier urged calm, agreeing to set up a joint inquiry into what caused the crash of Mr Garang's helicopter.
But correspondents say there is a real danger that a much-vaunted peace deal ending 21 years of civil war could be shattered by the sudden violence.
New southern leader Salva Kiir needs all the help he can get, says the BBC's Peter Greste in New Site, southern Sudan.
He has not even been sworn in yet as the new leader of the SPLM movement and holds no formal power.
That is why he asked church leaders visiting New Site to pay their respects to Mr Garang, to send envoys to Khartoum and appeal for calm, our correspondent says.
Both southerners and northerners have been attacked in Khartoum
"Enemies of peace may want to take the opportunity of the situation so that they don't allow the government and the SPLM to implement the peace agreement," Mr Kiir said.
"We want this situation to be stopped as soon as possible so that security returns to Khartoum and its suburbs."
Our correspondent adds that the southern administration is also hoping that a joint team of investigators will confirm the helicopter crash was indeed an accident and not an assassination, as some of Garang's followers suspect.
Local media say President Bashir is expected to attend the funeral.