Yasir Arman, spokesman for the former southern rebel Sudan People's Liberation Movement (SPLM), which will form a coalition government next week, also said leader John Garang will arrive in the capital on July 8 for the first time in more than two decades to take up the post of first vice president.
"The state of emergency is going to be lifted immediately on July 9," Arman told Reuters.
But consultations would follow to decide on the situation in eastern Sudan and the remote western Darfur region.
"There will be consultations about western and eastern Sudan, about whether emergency law will remain or not, between the president and the first vice president," he said.
According to the new constitution, due to be ratified by July 9, the president and first vice president can decide to initiate any state of emergency, which would need parliamentary approval, Arman said.
The government signed a peace deal with the SPLM in January, which ended more than two decades of civil war in Sudan's south. It provides for a coalition government, wealth- and power-sharing and democratic elections within three years. The south will also have a referendum on secession after six years.
The deal did not cover a separate revolt in western Darfur or a smaller conflict in the impoverished east, which has recently escalated with rebel attacks on government forces.
Arman said the SPLM welcomed the Thursday release from prison of opposition Islamist Hassan al-Turabi. He said Turabi's Popular Congress Party would be free to work legally as an opposition political party if it chose to do so.
Turabi, a former ally of President Omar Hassan al-Bashir, was imprisoned last year after his party was accused of attempting to overthrow the government.