Despite a slight easing of interest rates which caused a dip in early trading, the U.S. dollar remained strong in foreign markets yesterday. Gold, meanwhile, turned weak again, closing in major markets under the $500 level.

Market analysts said the the dollar was staying within fractions of last week's highs in part because investors expect the Reagan administration to mount a successful attack on inflation. President Reagan plans to report on his tax - and budget-cutting proposals -- at least in general outline -- in a nationwide television address on Thursday.

Administration officials predict that the dollar will continue on a strong course, even though their hope and expectation is that high interest rates -- a major factor in the recent strength of the dollar and slide in the price of gold -- eventually will come down.

Treasury Undersecretary-designate Beryl Sprinkel explained that, "once markets begin to believe our message," confidence in the growth and stability of the U.S. economy will insure a strong dollar and eliminate the fluctuations of the recent past.

Another optimistic note was sounded by Bank of England Governor Gordon Richardson, who told the Overseas Bankers Club in London that the worst of the world economic recession was over, meaning that real growth could resume later in 1981.

But he added: "Few of us think that the world economy will surge ahead rapidly, for there remain major potential constraints on economic growth."

In a speech last week in New York, Federal Reserve Board member Henry Wallich said that "at a time when fighting inflation is our number-one priority, maintaining the strength of the dollar internationally becomes an important objective."

Wallich said the the Fed's new strategy for controlling the money supply "should create expectations and conditions fundamental to a stronger dollar."

In London the dollar's strength and Prime Minister Margaret Thatcher's weekend hint of a cut in the minimum lending rate soon pushed the pound down to $2.3490 from Friday's $2.3670.

The Swiss central bank raised its discount rate to 3 1/2 percent from 3 percent and its Lombard rate to 4 1/2 percent from 4 percent, saying that differences between official and market rates were making it difficult to effectively conduct its monetary policy.

European closing rates with late New York prices in parentheses:

Frankfurt, 2.1220 marks, up from 2.1160 marks (2.1280); Zurich, 1.92375 Swiss francs, up from 1.9207 (1.9225); Paris, 4.89275 francs, up from 1.8775 (4.8960); Brussels, 34.0750 Belgian francs,down from 34.10 (34.11); and Milan, 997.45 lira, down from 1002.81 lira (1.0008).

In Zurich gold closed at $493.50 an ounce, $13 lower than Friday's close of $506.50. At the close in London gold had recovered to $496.50, still down $10 on the day.

In New York gold plunged to $485 an ounce from $501.50 Friday. Silver closed at $12.85, down from $13.30. The Commodity Exchange settlement price for gold was $482 compared with $501.70 on Friday, and the silver settlement price was $12.82 an ounce, down from $13.25.