The announcement on Saturday by Major General Paulino Matip, commander of the Southern Sudan Defence Forces, was unlikely just two weeks ago, when the vice presidency was held by John Garang de Mabior.
Garang and Matip had a number of differences over southern issues, particularly security.
Garang died in a helicopter crash on 30 July and was succeeded by Kiir, former commander of the Sudan People's Liberation Army.
In his inaugural speech on Thursday, Kiir expressed his desire to reach out to southern military and political factions.
Matip, who had stayed away when Garang was in power, was one of hundreds of delegates who greeted Kiir at the Khartoum airport on Wednesday, receiving a warm embrace, attended his inauguration, and met with him both Friday and Saturday.
"Salva Kiir has a vision different from that of late John Garang and has announced willingness for dialogue with the military factions and for this reason we are willing to participate in the upcoming south Sudan and national unity governments," Matip told a news conference after meeting Kiir.
He said south-south dialogue would resume soon in Nairobi "to seek solutions to the standing issues between the two sides".
Garang died in a helicopter crash
on 30 July
"The coming period begins today when we met with Kiir, so that the coming phase in the south would be that of peace and security," he said.
Previous talks between the SPLM and SSDF broke down over a number of issues.
Under the Comprehensive Peace Agreement, all militias must be dissolved and join either the government forces or the SPLA, which will become the security force of southern Sudan.
The late Garang had angered Matip with his harsh line against the SSDF, saying it would be "disciplined" if it did not agree to the terms.
"We insisted that we should take part in the security arrangements in the south, in the southern Sudan government and at the national government," SSDF spokesperson Brigadier General Garoth Garkouth said.
"The fact that (Kiir) has received us and agreed to talk to us is a sign that he is ready to listen to us and to involve us in the security arrangement and in other arrangements."
Matip said he had no personal issues with Garang but preferred Kiir's method of implementing the same agenda.
South Sudan unity
Kiir wants to "unify the southern Sudan first, put the southern Sudan in order, unify it, and then move to the greater compound - the Sudan," Matip said.
He said Kiir had agreed to a field visit of SSDF areas in the south "so that we will make it clear that all the past has been put behind us".
"The fact that (Kiir) has received us and agreed to talk to us is a sign that he is ready to listen to us..."
The SSDF is believed to have nearly 50,000 troops in the south.
The group split from the SPLA in 1991 and signed a peace agreement with the Khartoum government in 1997.
They remained independent but pro-government, and Khartoum is believed to have armed the group to keep the SPLA away from the oil-rich Bentiu area and other parts of the Upper Nile region of southern Sudan.
The group is supported mainly by the Nuer, southern Sudan's second-largest ethnic group.
The SPLM is led mainly by members of the larger Dinka tribe, including both Garang and Kiir.