The dollar skidded on European money markets yesterday but rose in New York amid signs that interest rates may remain firm and amid trader optimism in advance of President Reagan's speech to Congress outlining details of his economic program.

Gold rose to $505.50 an ounce in Zurich from $501 Tuesday and fell to $497.50 in London from $503.75. In New York it dropped to $493.00 from $501. The Commodity Exchange settlement price was $492.70, down from $499.

Silver slid to $12.80 an ounce from $13.18, and its Comex settlement price was $12.75 compared with $13.090.

In London the pound rose to $2.2665 from $2.2640 Tuesday and it fell to $2.2677 in New York.

In Tokyo, heavy buying of yen pulled the American currency lower to close at 206.55 yen compared with 207.45 on Tuesday. It rose to 206.80 in U.S. trading.

Other European closing rates with late New York prices in parentheses:

Frankfurt, 2.156 marks, down from 2.202 Tuesday (2.177); Paris, 5.0025 francs, down from 5.0900 (5.0625); Zurich, 1.9575 Swiss francs, down from 1.9975 (1.980); Brussels, 35 Belgian francs against 36.30 (35.02); and Milan, 1029.95 hre against 1039.95 (1034.00).