Saudi Arabia, apparently responding to new requests from President Carter, said yesterday it will continue to produce 9.5 million barrels of oil a day through the end of the year.

The Saudi decision, announced yesterday in Jeddah by Crown Prince Fahd, will continue to ease the light world oil supply and could have a dampening effect on petroleum prices.

The Saudis first increased production above their official 8.5 million barrel a day ceiling in July, also in response to a request from President Carter, whose political fortunes were being buffeted by long gasoline lines around the country. The time period for that increase was to have run out next Monday.

Both yesterday's announcement as well as July's were couched in terms of Saudi concern for the "interests. . . of friendly nations" and the world economic situation. But analysts of Middle East affairs have noted a recent increase in statements by prominent Saudis, both publicly and in private, that they expect U.S. policies, particularly in the Middle East, to be more closely aligned with those of Saudi Arabia.

Saudi Arabia is the world's leading oil exporter and America's largest supplier.

In a statement issued by the White House yesterday, President Carter called the Saudi announcement "constructive," adding that "it should help to stabilize prices in the world oil market."

The Saudi announcement caps months of intricate and occasionally awkward diplomatic consultation between the Carter administration and the Riyadh government.

Following the massive price increase announced by the Organization of Petroleum Exporting Countries at its June meeting in Geneva, Carter sent a personal message to the Saudis calling on them to lift production above their 8.5 million barrel a day ceiling.

Carter's request was answered in early July when the Saudi Press Agency quoted "a source in the royal court" saying production was being increased above the official ceiling during the third quarter for "budget reasons."

Earlier in the year, when the revolt against the shah shut off Iran's oil exports, the Saudis also increased production to 9.5 million barrels a day or more to make up for the shortfall.

According to a senior administration official, U.S. Ambassador John West "has been making continuous representations on behalf of President Carter." State Department officials were more cautious, saying only that West had been instructed to stress the instability in world oil markets that could result from a cutback in Saudi production.

Washington Post special correspondent Jim Landers reported yesterday from Jeddah that Carter's personal message to the Saudis earlier this year called on the oil-rich Persian Gulf state to raise production to 9.5 billion barrels a day through the end of the year. Further, both U.S. and Saudi diplomats had emphasized there was no "quid pro quo" in the president's request.

Privately, however, Saudi officials have continued to say they expect the Carter administration to press for a resolution of the Palestinian issue and the status of Jerusalem, both long-standing Arab goals in any Middle East settlement.

U.S. officials, both in the White House and at the State Department have continued to say that the Saudis have never officially linked oil policy with their demands for a Middle East settlement.

Nevertheless, in a blunt assertion of Saudi expectations that the United States will guide the Egyptian-Israeli peace negotiations toward meeting Arab world demands, Petroleum Minister Ahmed Zaki Yamani both before and immediately after the cartel's June meeting told reporters Riyadh's production was tied to a resolution of the Palestinian issue.

"I don't think you can expect the Arabs to cooperate unless there are positive political incentives," Yamani said.

Earlier this month the U.S. Embassy in Jeddah had reported that the Saudis were likely to extend their production increase through the end of the year. Those reports, however, said that the Saudi decision "could be influenced by political events in the Middle East related either to intra-Arab politics or the peace process."

World oil prices have increased nearly 60 percent since the beginning of the year, up from an average of $13.80 a barrel to the $20.77 a barrel price last week.

Riyadh, however, has continued to pursue its traditional moderate pricing policy.

The price of Saudi Arab Light, the "benchmark" oil used in OPEC, has risen from $13.34 to $18.00 a barrel. Other OPEC members are selling their oil at prices up to or in excess of the $23.50 a barrel ceiling adopted by the cartel in June.

In December the 13-member cartel is to meet in Caracas, Venezuela, to again fix prices and production policy. Many oil industry analysts expect that OPEC, will set a price rise that will at least match the inflation rate.

Saudi Arabia is the cartel's leading exporter, and it claims official oil reserves of more than 170 billion barrels, compared with 30 billion for the United States.

Spot prices on the influential Rotterdam market, while falling below the more than $40 a barrel levels during the Iranian shutdown early this year, still run well above the cartel's official prices.

In addition to expressing hopes that stepped-up Saudi production would stabilize prices and enable the importing nations to get through the winter without shortages, Prince Fahd also urged consuming countries to "take effective measures to reduce consumption and energy waste."

Yesterday, in a related development, the European Common Market countries and the United States announced in Paris that they would seek to hold down oil imports. Following through on a decision taken at the Tokyo economic summit, this spring, these major consuming nations also agreed to inform each other of prices and conditions negotiated on the spot market -- a move designed to check the upward movement in prices.