The U.S. dollar staged a moderate rally on European money markets late yesterday, although dealers said they were unsure why the dollar showed strength. Gold prices, reflecting the dollar's gains, declined slightly.

Trading was described as lively and steady, although not hectic, on most foreign exchanges. Operators advenced several theories for the dollar's stability over Monday's late rates, among them speculation as to the outcome of the Camp David summit meeting between Egyptian President Anwar Sadat, Israeli Prime Minister Menachem Begin and President Carter. Dealers said the market was "very nervous" and the only anticipation of possible U.S. moves to buoy the dollar had kept it from a steep drop.

A New York dealer said the market was "struggling for direction, awaiting further U.S. moves." The dollar weakened sharply in late afternoon, he said "when anticipated actions by the government failed to materialize."

Another dealer said, however, "It is apparent on the heel of a well-intentioned but futile attempts to defend the dollar that the Carter administration still fails to realize the international consequences of the dollar's deterioration."

Dollar rates in Europe late yesterday, compared with Monday's late rates, were:

Frankfurt, 1.9830 West German marks, up from 1.9775 marks; Zurich, 1,6180 Swiss francs, up from 1.6080 francs; Paris, 4.3398 French francs, up from 4.3160 francs; Amsterdam, 2.1525 Dutch guilders, up from 2.1245 guilders; Milan, 831.80 Italian lire, up from 829.60 lire.

In Tokyo, the only major world money market where the dollar declined yesterday, it took 189.80 yen to buy one dollar, down from 190.70 yen Monday.

In London, sterling finished the day weaker against the dollar. Dealers attributed the pound's decline to uncertainty whether or when Prime Minister James Callaghan will call new national election. It took $1.9409 to buy one pound late yesterday, compared with $1.94745 Monday.

Gold prices in Zurich and London, Europe's major bullion markets, reflected the dollar's modest rise. In London a Troy ounce of gold cost $209.75 at Tuesday's close, down $1.50 from Monday's late price of $211.25 an ounce. In Zurich an ounce sold late yesterday for $209.625 an ounce, down from $211.375 dollars Monday.