The Carter administration warned yesterday that another sharp rise in crude oil prices could push the United States and other industrial nations into a recession, and appealed to Saudi Arabia to increase its oil production to help ease current shortages.

Treasury Secretary W. Michael Blumenthal conceded at a news conference that a global recession would become "a possibility" if oil producers raise prices further. He said the impact of previous oil price increases already "is cutting into" consumer spending here.

Blumenthal also responded eagerly to a hint by Saudi Arabia earlier this week that it might temporarily boost its oil production if Western nations undertake a conservation program. He said the move would be "a tremendous contribution" to averting a recession in the West.

At the same time, the secretary acknowledged that the administration had "watched carefully" a modest decline in the value of the dollar in the past several days. The dip, which followed, but did not erase, a long recovery since last fall, obviously has worried U.S. officials.

Blumenthal said he thought much of the recent slippage stemmed from a drop in interest rates here, which brought them closer to those of Europe and Japan. "There will be no further such narrowing," he said. He called the underlying position of the dollar "very sound."

Blumenthal's comments marked the first time in recent months that a high administration official has publicly acknowledged that the oil-price situation might throw the economy into a recession. However, the secretary added that a serious downturn still was not "inevitable."

Just the same, he predicted that if crude prices rise any further, by 1980 the oil price increases already in effect will have cut economic growth in the United States by a full percentage point from what it would have been otherwise, while making inflation a percentage point higher.

The prospect of another price rise by the Organization of Petroleum Exporting Countries has been a major concern to Carter economic policy-makers. Many private forecasters believe the economy already is heading into a recession. A big oil price boost now could make that inevitable.

Officials also are known to be worried that the shortages and long gasoline lines here at home might further undermine compliance with Carter's voluntary wage-price guidelines program. As late as last Monday, some key advisers even suggested reviving some form of gasoline rationing. The idea still is on the table.

Meanwhile, the administration remained divided over what kind of major energy proposal to take to the Tokyo economic summit next week. The Treasury has come up with one plan, while the Office of Management and Budget is pushing a rival proposal.

The OMB measure would set up a new multinational body to coordinate government and private financing for efforts to make synthetic fuel. The Treasury has proposed establishing an international corporation with a $10 billion budget. Carter may propose an amalgam of the two.

At his news conference yesterday, Blumenthal reiterated the administration's position that, except for the prospect of another big oil-price increase, the economy "is not plunging into a major downturn." He said growth was slowing gradually, "in the right way."

However, he added, the threat of further increases in crude-oil prices is "one major overriding concern" to the administration. He said the oil-price boosts so far this year are "cutting into consumer behavior . . . Consumers do not have the money left" to buy other goods.

Blumenthal did not say yesterday why he was so certain that there would be "no further such narrowing" between interest rates here and abroad. Pressed on what that implied about future money and credit policies of the Federal Reserve Board, he sidestepped the issue.

However, Anthony M. Solomon, undersecretary of the Treasury for monetary affairs, said later Blumenthal had meant that the United States did not expect West Germany to raise its interest rates further, as it has in recent months.

In a telephone interview, Solomon also said the Federal Reserve had kept "federal funds" rate - which influences short-term commercial rates - "on course, despite the recent reductions in the prime lending rates" of banks, meaning that monetary policy here is steady.

The developments came as, separately, the Commerce Department reported that the economy grew somewhat more rapidly during the first quarter of this year than indicated by its last estimate of overall output, while inflation was slightly more rapid than had been thought.

In a second revision of its statistics on the gross national proudct, the department said the economy grew at an 0.8 percent annual rate between January and March, rather that at its previous estimate of 0.4 percent. It also pegged the GNP price index at 8.9 percent, up from 8.8 percent.

The department also boosted its estimate of first-quarter corporate profits reporting that after tax profits rose by 7 percent during the period rather that 5.7 percent as estimated earlier. Profits from current production, however, declined by $7.9 billion.