Angry white farmers told Prime Minister Robert Mugabe today that law and order has broken down in parts of southwestern Zimbabwe and said that unless the government took immediate action many would leave their farms.

One farmer received heavy applause from fellow whites when he told the grim-faced Mugabe, who is touring the area, that "the Army is responsible for 90 percent of the problems in the area," because of its lack of discipline and "brutal" treatment of the local population, which is loyal to opposition leader Joshua Nkomo. Mugabe, who also serves as defense minister, has direct responsibility for the armed forces.

The Matabeleland area, the stronghold of Nkomo's minority Ndebele tribe, has been wracked by violence since Mugabe removed the opposition leader from the Cabinet in February and charged Nkomo's party with plotting to overthrow the government.

More than 2,000 well-armed dissidents who are former soldiers are believed to be at large in the area, and the government has accused them of responsibility for numerous killings, rapes, robberies and the kidnaping of six foreign tourists two months ago.

In an effort to find the hostages, two of whom are American, the government has clamped a dusk-to-dawn curfew on an area of about 5,000 square miles and banned any nongovernment vehicles, causing severe food distribution and transportation problems. Mugabe did not have any contact with Nkomo or leaders of his Patriotic Front party during his heavily protected two-day tour.

Last night he met in a relaxed atmosphere with a mainly white audience of business leaders and civil servants at the city hall in Bulawayo, capital of Matabeleland. This morning he talked here with 25 white farmers, who came from as far away as 100 miles to see him. He then flew to Filabusi, 125 miles to the southeast, where he saw more farmers and addressed a rally of his party, the Zimbabwe African National Union (ZANU).

Filabusi is an area of strength for his party in the province. At all the meetings he stressed what he said was the Patriotic Front's responsibility for the dissident activity and vowed that the government would clamp down on all unlawful elements.

Calling the farmers' complaints "urgent problems," Mugabe promised to send ministers to the area to work out solutions.

Hundreds of police and soldiers lined the 45-mile route from Bulawayo to Marula this morning, guarding intersections, bridges, culverts and other strategic points.

Zimbabwe's white farmers have profited from high producer prices and expanded markets since Mugabe was swept into power in 1980 in elections that ended white-minority political control in this southern African nation.

Many of the farmers have warmly supported him, although by their conservative nature they oppose his socialist policies. The white farmers in Matabeleland, however, have long identified with the Ndebeles.

Roy Sayers, head of the local farmers associaton, told Mugabe that his people are plagued by two "very serious problems:" the almost total breakdown of law and order in the rural areas and encroachment on their grazing land by peasants' cattle because of drought.

He said the farmers support the government, but "some farmers can't farm anymore because of the security situation. If there is not immediate action they will be forced to vacate their farms."

The farms owned by the 5,000 white farmers produce most of the food in Zimbabwe, one of the few African nations not dependent on imports to feed itself.