Sudan's new military leadership said it dissolved the state security apparatus today and ordered the arrest of ousted president Jaafar Nimeri's closest associates. Khartoum was said to remain calm following yesterday's coup, although an anti-Nimeri general strike was continuing.

Gen. Abdel Rahman Sawar-Dhahab, who seized power as Nimeri was en route to this Egyptian capital from a U.S. visit, met today with the American Embassy's charge d'affaires. Nimeri remained in Cairo.

A State Department statement said David Shinn, the charge, met with Sawar-Dhahab at the request of the general, who "expressed interest in the maintenance of continued good relations with the United States and appreciation" for aid provided in recent years.

[Shinn said "food, refugee and other forms of assistance will continue" and assured the general "that the U.S. government shares fully the desire for strong bilateral ties," the statement concluded. U.S. Ambassador Hume Horan, who had been in Washington for the visit of Nimeri, was returning to Khartoum, he added.]

U.S. and Egyptian officials had been increasingly concerned in recent months that Nimeri's erratic, crumbling government would end in a takeover by Libyan-backed rebels or radical young military officers.

Sudan, Africa's largest country, is considered a valuable strategic ally to the United States and a vital one to Egypt since it controls the upper reaches of the Nile River and borders the Red Sea.

The announcement that the man who made the final move is Sawar-Dhahab, 51, a longtime Nimeri deputy handpicked as commander in chief of the Army only three weeks ago, provoked conspicuous relief here.

"He is very easy to sit and talk with," said a senior Arab military officer who has met the general on several occasions. "I always felt that I was sitting with a priest. He made you feel quiet and calm."

A visiting U.S. congressman said after a meeting with Egyptian President Hosni Mubarak this morning that Mubarak personally persuaded Nimeri to remain here yesterday rather than return to Khartoum in any effort to regain power.

Rep. Mark D. Siljander (R-Mich.) said Mubarak is apparently "happy to support the new government," which has been careful in its initial communiques to assert its "relations of blood and unity of destiny with Sister Egypt." The congressman is the leading Republican on the Foreign Affairs subcommittee on Africa.

Another western source briefed by senior Egyptian officials described Nimeri's overthrow as a "status quo coup, not along the lines of Liberia or Ghana, where you had a bunch of sergeants or second lieutenants taking over."

"There is a lot of relief," this source said. "These are respectable people."

Sudan's official Suna news agency said its transmissions had been interrupted "because the masses of the people today decided to continue the political strike and civil disobedience until the state security apparatus was disbanded and all the figures of the defunct regime arrested and put on trial.

"We resume our transmission now that the state security council has been disbanded and all the prominent figures of the defunct regime have been arrested," said the agency. Sawar-Dhahab was quoted as saying that the Army had taken over state security functions.

Nimeri's first vice president and chief of the powerful state security, Omar Tayeb, was reported to be among those under arrest.

European diplomatic sources told news services that the coup did appear, as first reported, to have been bloodless. All Army units, including paratroops, were said to have rallied to the support of Sawar-Dhahab, and several of the professionals in the capital who led the general strike that sealed Nimeri's fate reportedly have gone back to work.

Khartoum remains cut off from regular communications. Telex and telelphones were shut down during the escalating unrest that began Wednesday. The airport was closed Thursday by the strike, and since yesterday by the new rulers.

The official Egyptian news agency characterized Sawar-Dhahab as religious, moderate, "intelligent and calm." He is associated with the Khatemia, a moderate Sunni Islamic group that shared domination of Sudan's political life with a Mahdist sect until Nimeri swept them aside in his 1969 coup.

Sawar-Dhahab is not expected to have much sympathy for the much more radical and fundamentalist Moslem Brotherhood that Nimeri brought into high government positions in recent years.

In the past, Washington and Cairo were Nimeri's strongest backers in his confrontations with neighboring Libya and Ethiopia. Egypt also helped shore him up against his internal opposition, sometimes militarily. With such support he weathered four major coup attempts and countless mutinies and plots during his 16 years in power.

But after several illnesses, Nimeri imposed his highly personal interpretation of Islamic law, including amputations, floggings and many executions, throughout the country in 1983. Soon he had a civil war in the largely Christian or animist south and rising protests in the north.

Late last year, Washington temporarily suspended almost $200 million in aid, and in February Egypt pulled out the last of the air defense forces it had sent last year.

An Egyptian official said this afternoon that by the time Nimeri left for Washington to win back the suspended assistance, his demise was expected both here and in Khartoum, although the exact timing and speed of it may not have been anticipated, and no one was certain who would fill the vaccum.

On the day of his departure, Nimeri announced an end to many subsidies on basic goods and a devaluation of the Sudanese pound, sparking the riots and protests that finally brought the Army into action against him.

Sawar-Dhahab's first communique said the armed forces moved "to stem bloodshed" in the face of the "deteriorating security situation and the extremely complicated political crisis."

The new government then promised to be an interim rule moving toward democratization and peace with the rebellious south.

From Cairo's perspective, Sawar-Dhahab could hardly be a more fortuitous replacement for Nimeri. He has longstanding ties here, according to military sources. Vocal support for the coup from Libya's Col. Muammar Qaddafi is dismissed here as opportunism, even though one of the new government's statements talks vaguely of "mending our relations with some countries, particularly the neighboring ones," which could mean Libya and Ethiopia.

Sawar-Dhahab "visits Egypt frequently with his family," one of his acquaintances here said. "I think he understands Egyptians, and they understand him.

"He is a very good man, well accepted by the intellectuals, by the religious people and the professionals," said the acquaintance. "He is very moderate and a man with clean hands -- that is, not corrupted."

But there are also voices of caution. A military analyst said the question remains of "who is behind him -- who are the young people behind him," because it is apparent Sawar-Dhahab did not act on his own.

According to this analyst Sawar-Dhahab played a major role as deputy defense minister in determining who would go to the military academy and who would get advanced instruction necessary for promotions. As a result several more junior officers are believed indebted to him.