President Reagan is not exerting pressure on the Federal Reserve Board to cut the discount rate, although he favors lower interest rates, deputy White House press secretary Larry Speakes said yesterday.

Speakes' comments came in response to reporters' questions about a story in yesterday's Washington Post quoting a senior administration official who said the time had arrived for a new round of coordinated interest-rate reductions on a global scale. The senior official said the cuts should be initiated by West Germany and Japan.

"I don't think the president is preaching intervention on the part of government to drive interest rates down," Speakes said. He said the president wants to "let the market work its will."

The administration official's comments were made after the government had reported that real gross national product had advanced at an annual rate of only 2.9 percent in the first quarter of the year, down from the original estimate of 3.7 percent.

The Commerce Department attributed the downward revision in the GNP figure for the first quarter to later data showing greater deterioration in the nation's trade deficit.

The adjustment in the GNP figure followed other reports indicating continued weakness in the economy.

The official predicted the GNP figures for April through June also would look weak, and cited declining commodities prices as additional evidence that the global economy needs a new thrust from lower interest rates.

"The global economy now looks sick," the official said.

Twice this year, the United States and several other industrial nations made a coordinated reduction in interest rates.

Federal Reserve Board Chairman Paul A. Volcker said in congressional testimony Wednesday that he and some of the other governors are reluctant to reduce rates again.

A Fed spokesman said yesterday, "I haven't heard" of any sentiment in the administration for another round of global discount rate cuts.