The dollar fell sharply on foreign exchange markets yesterday, reflecting an easing in U.S. interest rates, while gold traded briefly over $600 an ounce before falling back at the close.

In the first full day's trading of the new year, gold closed in Zurich at $597.50 an ounce up $8 from $589.50 last Wednesday. In London gold closed at $599.50, up $10 from Friday's close of $589.50.

In New York gold traded to $603 at mid-day before falling back to $594 at the close, still higher than Friday's $586.75. The Comex settled gold at $593.60 an ounce, up from Friday's $586.30.

Silver rose to $16.30 an ounce from $15.60 Friday and settled at $16.26 an ounce, up from $15.61.

In Tokyo the dollar plummeted to a near-two-year low, closing out the first session of 1981 trading at 201.40 yen compared with 203.60 yen last Wednesday and the lowest since Feb. 23, 1979. The Bank of Japan intervened to support the dollar.

In London the pound rose to its highest level since mid-November, closing at $2.4165 compared with Friday's $2.3815, and soared to $2.4245 in New York.