Gold prices hit new highs today while the U.S. dollar improved against most currencies in New York and European currency markets. It slipped against the yen in Tokyo and the pound in London.

Fears of another steep rise in world oil prices and a cutback in official supplies of gold drove the price of bullion in Zurich, Europe's leading gold trading center, to a record closing high of $255.375 an ounce. Monday's close was $251.125. The previous record closing high in Zurich was $252,375, set last Thursday.

Gold also hit a record closing high in London, Europe's second largest bullion market. It ended the day at $254.75, after reaching $255.50 at the afternoon fixing compared with $251.75 Monday. The previous record closing high in London was $253.375, set on Feb. 22.

Dealers in Frankfurt said the dollar's widespread gains were due largely to a prediction by U.S. Treasury Undersecretary Anthony Salomon that the U.S. trade deficit would shrink substantially in 1980.

London dealers said the market also was anticipating a favorable report Wednesday on U.S. industrial production.

In Frankfurt, the dollar closed at 1.9058 marks against 1.9000 at Monday's close. The dollar finished in Zurich at 1.7258 Swiss francs against 1.7190 Monday, at 4.4065 francs in Paris against 4.3910 at 31.4650 Belgian francs in Brussels against 31.2950 and at 850.95 lire in Milan against 848.95.

In London, the dollar closed at $2.0630 to the pound, down from 2.0440 Monday. In Amsterdam, it finished at 2.0690 guilders, unchanged from Monday.

In Tokyo, the dollar closed at 212.65 yen, down from 213.80 yen Monday.