The military government of Sudan announced in Khartoum yesterday that southern rebel leader John Garang was flying to the Sudanese capital for talks with Gen. Abdel Rahman Sawar-Dhahab, the military leader of the 13-day-old government. But Garang's lieutenants here called the announcement "a lie."

Rather than negotiating with the new Sudanese government, leaders of the Sudan People's Liberation Army here said the rebel movement had decided to wage war against the military leadership in Khartoum until it handed power over to civilians.

The report that Garang was headed for talks in Khartoum followed Sawar-Dhahab's announcement of a major concession to the rebellious south. The new government, he said, had decided to reunify the country's three southern provinces, reversing a June 1983 action by former president Jaafar Nimeri that played a major role in launching Garang's rebellion.

Reports from Khartoum said the new government was putting the south under a new military high commission for a one-year transitional period.

Claiming to speak for Garang, who they said was in southern Sudan, the rebel leaders here said their movement had begun its war with raids Wednesday against Sudanese Army garrisons in the south.

"How is it that we are fighting Wednesday against the government and Thursday our leader is going to Khartoum?" said rebel Lt. Col. Daniel Awet. He said the rebel movement's radio, which broadcasts from Ethiopia, will announce later today that the Sudanese government's announcement was a "trick."

It was unclear, however, whether Garang might not have moved to explore the new government's overtures without informing his lieutenants here.

The reported raids on Sudanese Army garrisons in the towns of Akobo and Tonj came eight days after Garang warned in a radio broadcast heard in Khartoum that the new military government had one week in which to dissolve itself.

"They thought we were bluffing. The seven days have run out, and we meant what we said," said Maj. Rick Mashar Teny, one of the four rebel leaders interviewed here. "We intend to fight until the junta hands over power to the people. It took us two years to occupy nearly the whole of the south. In two years' time, we will be in Khartoum."

Since 1983, the rebels, with the support of Libya and Ethiopia, have seized control of most of Sudan's three southern provinces. The rebels have shut down a large American oil operation in the south and halted construction on the 200-mile-long Jonglei Canal, Sudan's major Nile River irrigation project.

In what they described as an official statement of their movement's goals, sanctioned by Garang, the rebel officials said that the new government in Khartoum constitutes "interference" in a popular revolution against Nimeri's 16-year rule.

"On the morning of the coup something went wrong. The popular uprising was taken over by the military," said Mashar Teny. He said that the rebel movement considers the leadership of Sawar-Dhahab and his military council to be a continuation of "Nimeri's system."

The rebel leaders rejected any participation in the government of Sawar-Dhahab, who has made conciliatory statements toward them. They also said they will refuse any cooperation with the fundamentalist Moslem Brotherhood, whose leaders had exercised considerable influence in Nimeri's government until they were purged last month.

The rebel leaders said they will agree to the formation of a new government only if it consists of people drawn from their movement and from the professional organizations and unions that led the strikes and protests that brought down Nimeri's government on April 6. Until that occurs, said Mashar Teny, "we have an army that is big enough for a protracted, offensive war."

The two-year-old Sudan People's Liberation Army is made up of an unknown number of southern Sudanese, assisted by several thousand Sudanese Army deserters. (The leaders here refused to say how many men in arms their organization had, although published estimates have put it at 6,000 to 10,000.) The movement was triggered by several events in 1983, including Nimeri's decision to impose strict Islamic sharia law on the mostly Christian and animist south, his political division of the region, reversing a 1972 accord that ended an earlier rebellion, and a decision not to refine southern oil locally, but instead send it by pipeline to the Red Sea.

Garang, the rebels' top leader, is a southern Sudanese who studied agricultural economics and military tactics in the United States. He deserted the Sudanese Army in 1983.

Rebel leaders said yesterday that, as part of their war against the new Khartoum government, their movement will continue to block Chevron's oil operation in the south and will not permit any work on the Nile irrigation project.

"That work will not be started up until we say so," said Mashar Teny, adding that the U.S. government could hasten the development of Sudan and of Chevron's multimillion-dollar investment there by giving the rebels arms and equipment.

The rebel leaders denied that the goals of their movement were influenced by support from Libya or Ethiopia.

"This is a myth propagated in Washington. President Reagan sees all movements such as ours in East-West terms," said Maj. Alfred Ladu Gore, another rebel leader. "It is absurd to say that if Ethiopia is helping us, if Libya is helping us, then we are communists. Ours is an internal problem that has to be solved by the Sudanese people themselves," Gore said.

In Wednesday's reported raids on Sudanese garrisons, the rebel leaders here said that 23 Sudanese soldiers were killed and 15 wounded at Tonj. They could not supply figures for rebel losses or results of the other reported raid, at Akobo near the Ethiopian border.

The civil war in Sudan, along with severe drought, the influx of more than a million refugees from Ethiopia and Chad, and gross mismanagement of a government that now owes $9 billion in international debts, has led the country to the brink of economic and social disaster. The United Nations Children's Fund estimates that a million children will die this year in Sudan because of famine.

Asked what effect their declaration of war will have on the future of the people of their country, the rebels' Mashar Teny said: "The resources are there in the south -- oil, water, animals, farmland. We control the resources. We will put the country back in order."