Ministers from the Organization of Petroleum Exporting Countries agreed on quotas to cut production by 1.5 million barrel a day today and predicted that oil prices will rise soon as a result.

Saudi Arabia's oil minister, Ahmed Zaki Yamani, said that by trimming its production ceiling to 16 million barrels a day, just as winter approaches and oil companies seek to build up their stocks, OPEC can expect prices to move up as early as mid-November or as soon as "the oil companies begin to feel the flow is restricted."

Yamani, exuding a confidence that some oil industry analysts do not share, said that demand for OPEC oil is expected to rise to 19 million barrels a day in the next two months.

Shortly after the OPEC announcement, two U.S. oil companies, Ashland Oil Inc. and Conoco Inc., cut their posted prices for some domestic crude oil by as much as $1.75 a barrel in a move that could undermine OPEC's drive to prevent a break in world oil prices, United Press International reported.

In Washington, Energy Secretary Donald Hodel said that OPEC's attempt to "manipulate the market by setting artificially high prices or by seeking to fashion arbitrary restrictions on production is not in the interests of U.S. or other consumers, or, in the long run, of producers."

Yamani said that the new quotas are more than enough to reverse downward pressure on prices. "My only worry is not to see the cut become too effective so that the market price rises above the official $29 dollar price," he said.

But oil traders said they were skeptical about the impact of the new quotas because of widespread cheating by several OPEC members in the past and the cartel's consistent record of overestimating demand.

"OPEC has shown it can't manage the market by cutting production, so it will eventually have to cut the price," a Houston-based oil trader said. "And the longer OPEC waits, the worse the situation will get."

Other industry analysts pointed out that some OPEC members are already producing at levels well below their previous individual quotas. OPEC's total output now is "close to 17 million barrels a day," less than the old ceiling, according to the OPEC conference chairman, Indonesia's Subroto.

Saudi Arabia will absorb the biggest reduction, cutting 647,000 barrels from its previous 5 million barrel-a-day quota. But Yamani admitted today that his country is now pumping only 4.1 million barrels a day.

"We are prepared to reduce considerably from where we are now," Yamani stressed. "We will make sure that the price goes back up."

Yamani ruled out cutting prices instead of production, saying price cuts would prove disadvantageous in the long term for both producers and consumers. Even at $28 or $29 a barrel, he said, major new exploration and the development of existing oil fields have practically ceased.

Some OPEC states expressed chagrin about the possibility that important non-OPEC producers like Britain, Norway or the Soviet Union might pick up the slack of any OPEC cuts in output.

"It's not fair for these countries to benefit from our actions yet not participate in stabilizing the market," said Subroto.

But Yamani contended that rival competitors outside the cartel are not in a position, in terms of available capacity, to "substitute for the shortage we have created today."

He said another encouraging sign was that two non-OPEC states, Egypt and Mexico, whose oil ministers attended the three-day conference here as guest observers, have announced their willingness to reduce production in tandem with OPEC to help bring order to the market.

The primary threat to OPEC's strategy may come from within its ranks, if member states become impatient to sell their oil and engage in such tactics as offering secret discounts or surpassing their production quotas.

Yamani admitted that some members have exceeded their alloted quotas "by as much as 50 percent." Delegates said the guilty parties included Iraq, Libya, Indonesia and Venezuela.

But Yamani claimed that the dangers of such cheating have become more evident as the global oil surplus persists, adding that "we are sure this will definitely come to an end because lessons have been learned."

Such concerns ultimately prompted 11 of the cartel's 13 members to accept the reduced quotas.

Nigeria, because of its troubled economy and heavy debts, was exempted and allowed to retain its recent price reduction of up to $2 a barrel, but only "for the time being," Subroto said. Iraq also will be freed from cuts in current production even though it is pumping 400,000 barrels a day above its prescribed quota. Small producers such as Gabon, Ecuador and Qatar were asked to make only token reductions in output.

Apart from Saudi Arabia, the bulk of curtailed production quotas was assessed against Kuwait, Indonesia, Libya, the United Arab Emirates and Venezuela.

In concluding their session today, the ministers deferred action on the complicated issue of price differentials, or the range of prices charged by OPEC for light and heavy crudes.

The Associated Press reported the following figures from Geneva. The daily per-barrel OPEC quota set in March 1983 is listed first for each country, followed by the amount of the new production cut.

Saudi Arabia: 4.975 million, 647,000; Kuwait: 1.05 million, 150,000; U.A.E.: 1.1 million, 150,000; Qatar: 300,000, 20,000; Iran: 2.4 million, 100,000; Iraq: 1.2 million, none; Libya: 1.1 million, 110,000; Algeria: 750,000, 62,000; Nigeria: 1.3 million, none; Gabon: 150,000, 13,000; Venezuela: 1.6 million, 120,000; Ecuador: 200,000, 17,000; Indonesia: 1.3 million; 111,000.