Zaire's President Mobutu Sese Seko, by calling on his friends and allies in Africa and Europe, appears to be gaining control over the Katangan invasion, the most serious threat so far to his 11 years of authoritarian rule.

Thanks to a timely French airlift of 1,500 Moroccan troops to threatened Shaba Province, the very real threat to his control of sprawling, mineral-rich Zaire has receded. Even his detractors in Africa have rallied round - or at least remained silent - for fear their own vulnerable regimes could suffer similar fates.

The official Zaire news agency AZAP today said that government troops launched a strong offensive yesterday against the rebels and that elements of the Moroccan force joined the drive last night to push copper-mining town of Kolwezi.

The agency said arms, equipment and one prisoner had been captured. There was no independent confirmation of the reports although reporters returning from the area said about 400 Moroccan soldiers had left Kolwezi yesterday in the direction of the alleged fighting 25 miles to the northwest.

(Special correspondent Robin Wright, in a dispatch from Kolwezi, said that the three companies of Moroccan troops reportedly moved to the town of Kanzenze to back up the Zairian troops after a battle yesterday that resulted in the first large number of injuries. A local doctor said 40 men were taken to local hospitals.)

A major combined offensive has been expected in a week or so in any case in Shaba, formerly known as Katanga.

Mobutu's improved position, though, is due less to any positive deeds of his army than a major miscalculations by the Kantangan rebels, led by a disgruntled former police officer named Nathaniel Mbumba.

The rebels, a mixed bag army deserters, recruits from Shaba's dominant Lunda tribe and middle-aged veterans of the Katanga gendarmerie of the early '60s, apparently could have walked into Kolwezi during the four weeks following the March 8 invasion from Angola.

Their failure to do so remains a major mystery. So, too, does theirinability to link up with leftist guerrillas that control a region bordering on Lake Tanganyika. They might also have provoked trouble in Kinshasa or elsewhere in this country the size of the United States east of the Mississippi.

The expected offense could drive the invaders from the towns, railway lines and roads they now hold west of Kolwezi and send them back into Angola.

Even a protracted guerrilla was of attrition is a prospect that could allow the kind of fight-and-talk negotiations used during the Vietnam war.

For most of Zaire's foreign friends, Mobutu has once again become the providential man, the only one capable of saving the nation's unity. His political opposition apparently is minor and ill organized.

Zaire is considered of major importance in Africa not only because of its mineral wealth but through its strategic location - a giant with ties to the West capable of influencing the direction of the rapid changes sweeping the southern shank of the continent.

Angolan President Agostinho Neto's apparent motives in unlessing the Katangan rebels involve his feud with Mobutu that started when the Zaire army intervened unsuccessfully in the Angolan civil war on the side Holden Roberto's National Front for the Liberation of Angalo.

The Katangans were a major Angolan card in the complicated feud. Their presence was meant to deter Mobutu from backing other rebels trying to take over Cabinde, Angola's oil - Rich Enclave, and from allowing Holden Roberto's men to attack northern Angola from Zaire.

But even discounting the traditional temptation of launching a foreign adventure to cloak problems at home, Angola apparently thought its risks in the Shaba adventure were minimal. At the very least, the operation is thought to have been tolerated by the Angolans' Soviet allies, who since Mobutu first kicked them out of the country in 1960 have considered him a creature of the Americans.

The Soviets and Angolans seemed to have reasoned that overthrowing Mobutu could prove popular in Zaire. If the effort failed, the thousands of Cubans in Angola were quite sufficient to keep Neto in power. Officially, Angola denied any role in the Shaba invasion, which it insisted was simply a lont-festering Zaire internal problem.

The invaders sought to avoid involving Angola, Cuba or the Soviet Union in charges of outside aggression.

Despite Egyptian President Anwar Sadat's claims, the rebels were not thought to have brought tanks with them from Angola, much less heavy weapons or even vehicles. Rather, they apparently preferred to comandeer transportation once inside Shaba and rapidly began using the Benguela Railway to move men and material west toward Kolwezi.

The rebels, perhaps as few as 1,500 men at the outset with another 6,000 in reserve inside Angola, stayed out of sight during the day as a pecaution was not of the great accuracy in any case.

From sketchy reports pieced together from missionary and other sources, the rebels began organizing a rudimentary civil administration in the 12-by-180-mile territory under their control.

In recent interviews, Mobutu indirectly has conceded that Shaba's anomalous position as the money-spinning province, treated like a poor cousin, made it suitable terrain for rebels seeking popular support among kinfolk.

The continued closure of much of the Benguela railway, which was damaged during the Angolan was has meant increasing hardship for Shaba. The railroad carried Shaba's copperore to the Atlantic port of Lobito and brought in 30 per cent of the province's petroleum needs.

Even in the palmy days before the Belgians granted the country independence in 1960, the big money was invested in the capital of Leopoldville, now called Kinshasa, not in the mining province itself.

Analysts sifting through the rebel propaganda statements credit them with great sophistication. Rather than raise the spectre of another secessionist movement - recalling the violent first years of independence when three breakaway movements fought the central government - the rebels claimed to be detribalized socialist revolutionaries whose sole goal was to remove Mobutu from power.

When he seized power in a bloodless coup in 1965, it was with the undisguised blessing of the United States and major Western powers, fearful that the alternative to "the West's last card" was a pro-Chinese regime.

Four years of United Nations military presence here had given way to a Chinese-backed rebellion in 1964 that swept through the country until stopped by European mercenaries and the intervention of Belgian para-troopers dropped by U.S. Air Force planes at Stanleyville.

Mobutu initially did bring a modicum of stability to a country whose very name - the Congo - had become synonymous with anarchy and mindless violence.

Yet large areas remained out of the central and outside the money economy.

Influenced by trips to China and North Korea, Mobutu first seized foreign businesses and property and handed them over to Zaire citizens, then "radicalized" or nationalized many of them when his compatriots proved incapable of managing them profitably.

Last year he abruptly decided to invite the old owners to return with majority ownership and a free hand in management.

Before the drop in copper prices in 1974, Zaire had a $2 billion foreign debt - much of it in questionable prestige projects - which it later was unable to honor. Payments have been stretched out after protracted negotiations.

TheIMF, provided standby credits conditional on Zaire's willingness to return to financial and monetary orthodoxy. Foreign banks led by the First National City Bank undertook to raise a loan of $250 million in 1977 if Zaire continued to meet its interest payments and honor the IMF conditions.

War expenditures could well jeopardize the stabilization plan. The banking consortium's undertaking includes an escape clause that could be invoked in the light of the Shaba fighting to let it off the hook.