Kidnapers of an American missionary and 10 Filipino nuns asked $100,000 in ransom today. President Corazon Aquino, denouncing the demand, challenged her military to bring law and order "once and for all" to the southern island of Mindanao where the 11 were seized.

"It is the Army's turn to act decisively," Aquino said in a statement. "This festering problem has gone too far and too long. The government cannot be blackmailed, nor will it adopt a policy of appeasement toward kidnapers who have abused the military's attitude of tolerance."

Aquino demanded that the military "settle once and for all Lanao's problem of warlordism and banditry," a reference to Lanao del Sur Province.

Earlier, Defense Minister Juan Ponce Enrile reported to the president that the Moslem rebels who abducted the Rev. Brian Lawrence, 30, of Madison, Wis., and 10 Carmelite nuns were demanding that, in addition to the ransom, the government grant full autonomy to the Moslems on Mindanao.

Enrile said the rebels' demands were delivered by the son of a Moslem officer who had deserted from the Army. Enrile identified the officer as one of the leaders of the armed group that seized the missionary and the nuns in two separate incidents Saturday in Marawi, the spiritual center for the Philippines' 5 million Moslems. It is about 500 miles south of Manila.

Enrile said the kidnapers' leaders are commanders of the Moro National Liberation Front, an armed movement that in the mid-1970s waged a war of secession against the government of president Ferdinand E. Marcos.

The war, one of the bloodiest in the history of this overwhelmingly Roman Catholic nation, cost an estimated 50,000 lives. Afterward, most of the rebel leaders became close allies of Marcos, who in 1976 signed a peace treaty that granted the Moslems far-reaching autonomy in Moslem-majority regions of Mindanao.

The rebel leaders, most of whom have remained fiercely loyal to Marcos even though he was driven from office in February, are now demanding full implementation of the accord.

Marcos granted political autonomy to the Moslems in 13 provinces of Western Mindanao and on the island of Palawan, but neither he nor Aquino has permitted the Moslem leaders to form an autonomous Islamic army, as provided for in the agreement.

Marcos did allow several of the Moslem leaders to maintain private personal armies, but Aquino has asked the Army to disarm and neutralize them.

Enrile said Lawrence, who was working as a missionary at a university in Marawi, had been kidnaped because the Moslem rebels were angry with local officials for failing to pay $1,000 they had promised as ransom in an earlier kidnaping of a French priest.