Fiat, Italy's largest private company, is engaged in an unprecedented test of strength with the country's powerful labor unions over workers' violence that the giant auto maker claims has produced a "climate of tension and terror" in its plants.

The issue came to a head when the company decided to suspend 61 workers Tuesday for actions causing "moral and material damage." The move produced negative union reaction that led Fiat the next day to suspend all hiring.

Because of Fiat's size and economic influence, the conflict could have a significant effect on both industrial labor relations and Fiat's own economic health.

Spokesman for fiat in Turin have said that the company is willing to undergo short-term losses in production if long-term improvements in the work atmosphere can be made.

"If we are unable to establish a minimum of order, the alternative will be either collapse or closure," industrial relations chief Cesare Annibaldi told reporters.

During the last four years Fiat, its executives and other representatives of management -- shop foremen in particular -- have been subject to growing violence from left-wing terrorists operating in Turin, Naples and other areas and from extremists inside their factories.

Since 1975 three Fiat executives have been shot and killed, and 19 others have been wounded in terrorist ambushes. There were 18 cases of arson of factory premises, and the private cars of at least 18 management representatives have been burned.

The most recent incident of terrorist violence came a week ago when urban Red Brigades guerrillas shot labor relations official Cesare Varetto in the legs in front of his wife and child. Three weeks ago, a top level Fiat executive, Carlo Chiglieno, was murdered by terrorists as he left his Turin home for work.

But according to Fiat officials, only the most dramatic incidents have become publicly known. The complain of daily incidents of violence within the factory against officials. The suspension letters issued this week were accompained by a statement saying the company cannot differentiate between "the criminal acts that cause woundings and murders and those acts that go beyond the limits of a civilized confrontation between the social parties and end up by contributing toward a climate of tension and terror."

Fiat sources speak of daily violence within the factory involving Mafia- type warnings and intimidation, revenge, and physical and moral violence. Insiders at Fiat said that such violence occurred during frequent wildcat strikes or work stoppages as well as during the normal course of daily work.

The unions, and several leftist Italian political parties, reacted sharply to the suspensions, claiming that the charges included in the letters of dismissal -- which did not directly accuse the recipients of taking part in terrorist activities -- were vague and unsubstantiated. A three-hour strike, only partially adhered to, was called on Wednesday, a general workers assembly has been scheduled for next Tuesday, and an appeal has been made to Premier Francesco Cossiga to have the layoffs rescinded.

"This is an attempt to recreate a climate of fear within the factory," said a joint communique by all of Italy's major unions that asked Fiat to specify the charges against the 61 persons fired.

Italy's labor unions are strongly antiterrorist, but Fiat officials believe they have not acted sharply enough against the widespread violence that now exists in many major Italian factories.

With a work force of 270,000 people and 150 factories throughtout the country, the Fiat complex has always been one of the most active in Italy. Last year the company's total turnover amounted to about $18 billion. But company spokesman say strikes, wildcat work stoppages, absenteeism and fear on the part of shop foremen has led in recent years to a drastic decline in productivity.