Garang, a key figure in a January peace deal hailed as a rare success story for Africa, died over the weekend after the Ugandan presidential helicopter he was travelling in went down in bad weather.
"We are meeting to decide the management of a national crisis that has befallen us and to chart the way forward," Pagan Amun, a senior SPLM official, said at SPLM's headquarters in New Site.
"We are mourning, but we have the courage to move on."
Six of Garang's companions and a crew of seven also died in the crash near the Sudan-Uganda border, Khartoum said on Monday, though a member of the southern Sudan leadership council said 17 bodies were recovered.
The meeting of 21 leaders from the political wing and military command of the SPLM/A was chaired by the deputy leader and Garang's probable replacement Salva Kiir.
Garang's body, draped in the southern Sudan flag, was lying on a bed inside another room in a one-storey brick building guarded by SPLA soldiers.
John Garang's wife, Rebecca,
said his vision lived on
A small truck offloaded two coffins which were moved by SPLA officials into the building, witnesses said.
Garang's wife, Rebecca, called for calm and said she was confident the SPLM leadership would pick Kiir to replace her husband.
"I think the leadership will support him and so do I," she said, flanked by three of her six children. "It is just my husband who has died. His vision is still alive."
She said she was not going to apportion blame for Garang's death, adding she was in communication with world leaders including Uganda's President Yoweri Museveni and was waiting to take a call from US Secretary of State Condoleezza Rice.
Garang's wife, who often travels with her husband and was meant to go with him to Uganda but stayed behind at the last minute, said the funeral arrangements would be decided by the SPLM leadership and the government in Khartoum.
"This was his day and I accept that God has come to collect him," she said after attending a prayer service with some of her sisters and other family members under a tree.
Garang had left Uganda by helicopter late on Saturday to return to Sudan after talks with Museveni.
Various sources in Uganda and Sudan said it appeared his helicopter ran into bad weather, although there was also speculation it had run out of fuel.