The Algerian government faces a serious challenge from a general strike and rioting in Kabylia, the homeland of the Berbers, the country's largest minority.

Sources in Algeria report that the region's capital Tizi-Ouzou is closed to civilian road traffic and that the telephones also appear to be cut off since a day of rioting Sunday. The unrest was sparked by the takeover of the city's university and hospital by riot police Saturday.

Reliable sources said "a fair number" of people were killed in the takeover of the two centers of the general strike movement.

Students who went on a sympathy strike at the University of Algiers said 32 persons were killed, but official spokesmen denied that anyone had been killed or wounded.

Berber sources in Paris said that Saturday night military security agents rounded up the faculty of the Tizi-Ouzou University and the staff of the hospital and transferred them to prison in Algiers. This could not be confirmed, but other important parts of their accounts of events were fully confirmed by independent sources. Also unconfirmed was a Berber report of 200 persons being wounded Saturday night.

Trouble had been brewing for several weeks in Kabylia about Berber demands for recognition of their language and culture. Teaching of them has been banned since Algerian independence from France in 1962.

The Berber movement was largely nonviolent until Saturday. The movement had reached a high point with a successful general strike throughout Kabylia last Wednesday, which apparently prompted authorities to move on Saturday.

Berber sources here say the student leadership of the language movement is actually a cover for the party of Ait Ahmed, one of the original leaders of the Algerian independence movement. Under Ahmed's leadership, Kabylia revolted against the new Algerian authorities in 1963, and it took months for the government to quell the rebellion in the mountainous countryside.

The Berbers are descendants of the original inhabitants of North Africa before the Arab invasions. They number about 3 million of a total of more than 18 million Algerians.

A French citizen who slipped into Tizi-Ouzou Sunday and returned here yesterday said he had spoken to younger Berber leaders who said they were ready to take up arms. They also expressed contempt for Arab domination, which has forced on them such distant concerns as the struggle of the Palestine Liberation Organization, he said.

The Frenchman said he saw hundreds of students and workers demonstrating and throwing rocks at riot police armed with clubs. He said he did not hear shots or notice tear gas in the half day he spent in the town of about 60,000.

He said military police barred access to the university and the hospital Sunday, and the shops were all closed.

Another foreign traveler, who returned this morning from Algeria said the "Arab telephone," a system of word-of-mouth reporting, spread word of the troubles in Kabylia as far away as Tamanrasset deep in the southern Sahara Desert.

The traveler said that on return to Algiers yesterday, she found uniformed patrols and military checkpoints.

The unofficial reports, she said, also mentioned trouble in a number of other widespread localities far from Kabylia. A communique in Paris from the Berber-dominated Committee for the Defense of Cultural Rights in Algeria spoke of "blind repression" in the western cities of Oran and Sidi-bel-Abbes and the eastern town of Batna.