The recent cutoff of new Italian oil orders by Saudi Arabia has weakened Premier Francesco Cossiga's minority government and threatens to create serious economic problems for Italy, which is highly dependent on imported energy.

The Saudis cancelled a deal concluded last summer with the Italian state oil agency, ENI, for the sale of 87.5 million barrels of crude oil. The action was in response to repeated press reports here about alleged kickbacks to unnamed top Italian politicians. p

The transaction, which set an advantageous price of under $19 a barrel, was made through a middleman acting through a Swiss-based Panamanian company. It also involved a 7 percent commission amounting to over $120 million.

Speculation began here several weeks ago that part of the commission had gone to Italian politial leaders, but no hard facts have emerged.

Although there were no allegations of Saudi corruption, the continuing charges angered the Saudis and Saudi sources were quoted last week as saying, "We had to react . . . because our prestige was involved."

[From Jeddah, Washington Post special correspondent Michael Hall reported that the cancellation of the deal was not formally announced here. Hall quoted one Western diplomatic oil specialist as saying that although there are no indications that the cancellation will affect other Saudi government-to-government oil deals, "it certainly raises a lot of question."]

Italian officials were worried even before the Saudi action because their oil needs next year, estimated at about 721 million barrels, were running 20 percent ahead of guaranteed supplies.

Economists and Western diplomats here say that if Italian officials fail to convince the Saudis to reverse their decision, Italy's oil position in 1980 could show a gap of from 105 million to as much as 161 million barrels.

Data worked out for Guido Carli, president of the Italian national manufacturers' association, Confindustria, suggest that an oil shortage of such dimensions could bring gross national product down by 12 percent and put as many as 800,000 people out of work by next summer.

The oil gap could be filled by purchases on the spot market if the government were willing to take the controversial step of decontrolling the prices of oil products here. But, according to economist Paolo Leon, oil purchases at the 40 to 50 percent higher rates on the spot market would boost Italy's 18 percent inflation rate even higher and risk a serious recession.

In any event, some increases in the price of oil products appears inevitable and Italian ministers have already said that gasoline rationing can no longer be excluded. An expected 33 percent price hike that could raise the cost of gasoline to about $3.75 a gallon would cut sharply into household income. Sharply increased prices for heating oil would also jeopardize industrial production.

In addition, reliance on spot market oil would threaten Italy's current balance of payments surplus.

While top-level contacts attempt a reconciliation with Saudis, the cutoff has dramatized the scandal here and weakened the minority government set up only last August.

The allegations have primarily damaged the Socialists, whose votes in parliament assure the government's survival. The head of ENI, Giorgio Mazzanti, is a Socialist and most politically aware Italians believe the scandal story was begun by Socialist leader Bettino Craxi, who head a rival party faction.