Sudan, in a move certain to complicate further its increasingly troubled relations with Egypt, will ask this country to extradite former Sudanese president Jaafar Nimeri.

The move is being made by a Sudanese government under increasing public pressure to take action against Nimeri, whose government was overthrown in Khartoum by his top military officers April 6 as he stopped in Cairo on his return from a visit to the United States.

Nimeri, who had been in power for 16 years, was granted asylum the same day by Egyptian President Hosni Mubarak, who has steadfastly refused any suggestion that he might force his longtime ally to return to Sudan.

During a June 17 visit to Khartoum, Mubarak told the Sudanese press: "You may consider Nimeri an assassin or a criminal. That's your business. But the Egyptian constitution does not allow the president to extradite a political refugee."

The question of Nimeri's extradition became increasingly heated after a demonstration last Thursday in Khartoum by as many as 40,000 Sudanese demanding Nimeri's return.

The announcement of the new Sudanese government's intention to request extradition was reported today by the official Sudanese news agency. No date was set for the action, and both Sudanese and Egyptian officials declined to comment.

The new Sudanese ambassador to Egypt, Al Amin Abdellatif, told reporters in brief remarks earlier this week that if Nimeri does not want "to embarrass Egypt," he should go to "any other country."

Today, Abdellatif reportedly met for 90 minutes with Mubarak after formally presenting his credentials. Neither man made any public comment on the situation.

The extradition issue is coming to a head as U.S. and Egyptian officials are increasingly concerned about what is perceived as growing Libyan influence in Sudan.

On July 7, after a top Sudanese military delegation spent more than a week in Libya, Sudan announced that it has signed a military protocol for logistics support and training with Libya.

The move, which threatened to put Libyan leader Muammar Qaddafi in an influential position with the Sudanese armed forces, was regarded with consternation in Washington, which repeatedly has attacked Qaddafi for supporting international terrorism.

Sudan is the largest country in Africa, bordering the Red Sea and eight other nations. Under Nimeri it had become a vital strategic ally of the United States, and, since the coup, Washington has hoped to continue close relations with its new military and civilian government. But Qaddafi long has had designs on Khartoum.

During the latter part of Nimeri's rule, as Nimeri grew ever closer to the United States and to Egypt and more dependent on their aid, he and Qaddafi became bitter enemies. In 1981 Nimeri called for Qaddafi to be removed "by any kind of war, by taking him out, by killing him."

Qaddafi, meanwhile, made continuous overtures to the Sudanese army and the Sudanese people to overthrow Nimeri.

When Nimeri fell, it appeared to be the result, not of Libyan maneuvers, but of popular revulsion with a government that many claimed had led the country to bankruptcy, starvation and civil war. Qaddafi was quick to try to take advantage of the change.

In an interview here Tuesday night, one of the most prominent Libyan exile leaders suggested that despite Qaddafi's efforts to exploit the current situation in Sudan, he is unlikely to have much immediate impact.

Former Libyan prime minister Abdulhamid M. Backoush suggested that Qaddafi, who reportedly has sent hundreds of his agents to Sudan since the coup, has the capacity to carry out serious terrorist actions there.

Backoush and Egypt last year handed Qaddafi one of the most humiliating defeats he has ever suffered by tricking Qaddafi into announcing Backoush's assassination as a "traitor, hireling and stray dog" when in fact Backoush is alive.

Backoush also suggested that Qaddafi has no real political base in Sudan and little hope of building one. While he reportedly has supplied southern Sudanese rebel leader John Garang with funds, Qaddafi has not shown any real interest in stopping the fighting in the non-Moslem south.

By signing the military protocol with Libya, Backoush said, "The Sudanese government is trying to calm Qaddafi down," adding, "Nothing will work between Sudan and Libya for sure.