Garang, leader of the Sudan People's Liberation Movement (SPLM), met Egyptian President Hosni Mubarak in Cairo on Wednesday and briefed him on the progress of talks between his group and the Sudanese government, especially the drafting of a new constitution.
Darfur rebel leaders told Garang in April that they would approach the discussions with the government "without any preconditions".
"I believe they have already set 10 June as a date for the meeting," he told reporters.
The conflict in Darfur in western Sudan broke out in February 2003 after regional tribes took up arms, complaining of discrimination by Khartoum.
The government is accused of responding by backing a scorched-earth counter-insurgency by militias known as the Janjawid.
War-induced hunger and disease
have killed over 180,000 people
War-induced hunger and disease have killed more than 180,000 people, according to UN estimates. Around two million others have fled their homes.
The two main rebel groups in Darfur - the Sudan Liberation Movement and the Justice and Equality Movement - met in Libya last month with local leaders from the north, south and west Darfur regions and pledged to resume talks with the government.
The SPLM and the Sudanese government signed a peace deal in January and made Garang a first vice president, clearing the way for the drafting of a new constitution that would give southern states the opportunity to vote on secession in six years.
Garang said talks about the new constitution that began in April were "going well and we hope that we will finish it before middle of June and then be approved by parliament and the SPLM to pave the way for the formation of the national government by 9 July".
He said arguments over the Islamic wording at the top of the draft constitution were resolved by presenting two versions.
The one for the north will keep the original text but the one for the south will not carry the words "In the name of Allah the Merciful, the Compassionate", an Islamic invocation that normally precedes Islamic texts, statements and political declarations.
"The UN food pipeline is virtually empty and people are actually starving to death in some places in southern Sudan. It is a horrific situation"
Sudan first vice president
Sudan's north is predominantly Muslim but the south is a mix of Christians, Muslims and animists.
But Garang warned that the return of millions of refugees to their homes in southern Sudan following the war's end would create a humanitarian crisis worse than the tsunami that swept southeast Asia in December last year.
"We expect some three million people to return to southern Sudan from the north and another million from neighbouring countries, that's more than the Tsunami [crisis]," Garang said.
"The UN food pipeline is virtually empty and people are actually starving to death in some places in southern Sudan. It is a horrific situation."