Leaders were calling on the Sudanese people to stay calm in an effort to contain violence that started on Monday.
"In Khartoum, 111 people are confirmed dead by the Sudanese Red Crescent, while 345 people were injured and evacuated from the scenes of violence," Paul Conneally, communication coordinator for the International Committee of the Red Cross, said on Thursday.
The death toll, he added, was expected to rise given the high number of those injured.
In a national address on Wednesday, President Umar al-Bashir called on the Sudanese people to exercise vigilance and self-restraint, the Sudanese news agency reported.
He also issued a decree establishing a national committee - in cooperation with the Sudan People's Liberation Movement/Army (SPLM/A) - to investigate the causes of the helicopter crash that occurred near the Ugandan border.
Nhial Deng Nhial, senior leader of the SPLM/A, said in a statement his movement considered the violence a direct threat to peace. He called for fortitude and wisdom in resolving and containing "these irresponsible actions".
"We would like to express, in the strongest possible terms, our total rejection of all the destruction and the infringement on the lives and properties of peaceful citizens," he said.
Jan Pronk, the Special Representative of the UN Secretary-General in Sudan, told reporters in Khartoum that while many people were angry and frustrated over Garang’s death, there was no need for rioting and that they should stop.
"I call on everybody, the opinion leaders, the police, the leaders of the communities, on fathers and mothers at home, also on young people who are leaders amongst themselves, to come to their senses," Pronk said.
Garang's wife, Rebecca, said in a statement carried by the Wednesday edition of the Khartoum Monitor: "If they loved him, they should remain calm and carry on with his vision. It is John Garang who is dead. The vision should be kept alive."
The Khartoum suburbs of Hajj Yusuf, Omdurman and Fithi Hab, and Kalatla and Mayo camp for internally displaced persons (IDPs), were the most unstable areas of the city while the centre of the capital seemed relatively calm, Conneally noted.
"The Sudanese Red Crescent is doing an excellent job and have more than 100 volunteers working in neighbourhoods and IDP camps where the violence was most intense," Conneally noted.
"The military are deployed in most of these areas and the police is fully deployed all over Khartoum," he added.
The governor of Khartoum State, Abd-al-Halim Ismail al-Mutaafi announced on Wednesday that the security authorities had detained over 1,450 people on suspicion of involvement in the acts of violence that rocked Khartoum.
In the southern town of Juba, the Sudanese Red Crescent had confirmed that 13 people were killed and 20 injured, Conneally said. The capital of Upper Nile State, Malakal, counted six dead and 37 injured.
"The situation in Juba calmed down somewhat," a local source said on Thursday. "Although there is still sporadic shooting and fighting - at night - and heavy military presence in the streets."
"On Monday, the situation was very explosive," he added. "The sky was all black with oily smoke, there was shooting, and they burned down the two main markets in Juba."
Garang's sudden death has raised fears, especially among southern Sudanese, that the commitments made in the Comprehensive Peace Agreement (CPA) to end the 21-year civil war between Garang’s SPLM/A and the Sudanese government, could be jeopardized, analysts said.
Pronk said he was pleased with the reactions of the government of Sudan and the SPLM/A and their desire to continue with the implementation of the CPA.
He noted that the fact that there was no jockeying for power within the SPLM following Garang’s death was a very good sign of the maturity of the SPLM/A.
The SPLM nominated Salva Kiir Mayardit as its new chairman and proposed him for appointment as the new First Vice-President of Sudan. Pronk said Kiir had been with Garang from the beginning, and was - as a military commander- well respected in both the north and the south.
"He is the right choice," Pronk said.
Garang died on Saturday en-route to southern Sudan from Uganda, following a meeting with President Yoweri Museveni. Sixteen other people who were travelling with him in the Ugandan military helicopter also died.