Saudi Arabia said yesterday that it would not increase oil prices this quarter, breaking a pattern of sharp price increases announced by other exporting nations since January.

While not ruling out future price hikes, the Saudi Royal Court said it is holding down prices "out of its grave responsibilities toward international economic stability," and called for a meeting of oil producers and consumers.

The statement by the world's leading oil exporter came on the heels of Kuwait's announcement Monday that it is increasing prices 9.35 percent above the oil cartel's official level.

Asked yesterday about price increases by six of the 13 members of the Organization of Petroleum Exporting Countries as a result of the Iranian oil shutdown, President Carter said, "We have no control over it. We deplore it."

At his news conference yesterday afternoon, Carter went on to say that the administration will continue to use "legitimate influence" to hold down prices. Carter also said he will send specific plan to Congress to deal with the Iranian oil shutdown in the weeks ahead, but in the meantime, will not place "stringent restraints" on the economy.

Monday, the White House sent details of standby gasoline coupon rationing and mandatory conservation plans to Congress. But Carter and Energy Secretary James R. Schlesinger Jr. yesterday both ruled out immediate conservation measures to cope with the loss of Iranian oil. The 9-week-old Iranian oil shutdown has reduced the nation's imports by 5 percent and world oil supplies by 2 million barrels a day.

At the State Department yesterday, officials said the Saudi announcement was a welcome sign. These same officials, however, said it does not allay the administration's growing fears that OPEC will increase prices in one form or another at its March 26 meeting in Geneva.

Referring to "several scenarios" for higher prices, a State Department official said yesterday that OPEC could increase its official prices for oil at the March meeting above the 2-month-old 14.5 percent increase announced in December at Abu Dhabi for 1979. OPEC could also agree to raise prices uniformly on premium oil, as Abu Dhabi did Feb. 15, or on oil products as Venezuela did Monday. Or it could raise prices on "incremental production" above normal levels, as Saudi Arabia did Jan. 15.

These fears are mirrored through-out the oil industry. Walter J. Levy, an international oil analyst, says, "Prices now are a much greater threat than the supply problem."

Another respected analyst, Larry Goldstein of the Petroleum Industry Research Foundation, agrees. "Logic tells me there will be an increase in March and there are ever-decreasing chances that there won't be," Goldstein told a reporter.

Carter, however, said yesterday that the United States is better organized to deal with the Iranian oil squeeze today than it was before the 1973 Arab oil embargo. Schlesinger told a morning session of the National Governors' Association that the administration is taking painstaking efforts not to "over-react" as the Nixon administration did in 1973.

In his talk, the energy secretary went on to warn that energy prices will continue to increase as a result of the Iranian shortfall, with gasoline costing as much as 10 cents a gallon more by the end of 1979, rather than the 7 cents a gallon DOE had forecast earlier.

In a related action yesterday, Mobil Oil Corp. announced that it was joining other major oil companies such as Shell Oil, Atlantic Richfield, Standard Oil of California and Continental Oil Co. in "allocating" gasoline -- in effect, rationing supplies -- to their customers. Mobil's allocations to its customers begin March 1.

Schlesinger said, "There is no clear indication that Iran will not come back." Yesterday, in Tehran, Hassan Nazieh, the new head of Iran's national oil company, said the cartel's former second largest exporter would begin selling oil next Monday.

Cataloging a now familiar set of options, Schlesinger told the governors that the administration can offset lost Iranian production by increasing use of natural gas, lowering environmental standards to burn coal and highsulfur fuel oils, stepping up production from the Elk Hills Naval Petroleum Reserve in California and from Alaska's North Slope and reducing the pace of the lead phase-out mandated by the Environmental Protection Agency to reduce gasoline demand.

"The total savings involved from these initiatives woud certainly be able to carry us through," Schlesinger said.

Yesterday, Schlesinger also wrote the Federal Energy Regulatory Commission, calling on it to issue rules that would increase the use of surplus natural gas in place of oil.In a letter to FERC Chairman Charles Curtis, he said the encouragement of sales of surplus gas from producers and intrastate pipelines is "particularly critical" now.

Still another step the president can take would be to seek implementation of the International Energy Agency's sharing plan at a conference of the 19-industrial-nation group in Paris Thursday and Friday.

Assistant Energy Secretary Harry E. Bergold Jr. said that "we do not anticipate a triggering under anything like the current situation."

John Treat, a DOE international oil specialist, told the Senate Energy Commitee yesterday that it would take nearly a 5-million-barrel-a-day shortfall in the free world -- versus 2 million from Iran -- to result in an automatic triggering of the IEA sharing agreement.

The total consumption of the IEA countries is 37 million barrels a day.

Bergold also said that major oil companies such as Exxon have started allocating oil voluntarily along the lines of the IEA plan. The plan is designed to spread the losses evenly by basing them upon total consumption rather than on the level of imports.

The biggest question in the world oil market still is whether Ayatollah Khomeini's Iranian government can return his troubled nation to the ranks of the oil exporters. So far, one State official says, that question is still "untested."