The high-flying American dollar continued to soar to new heights against most major currencies yesterday. The British pound fell below $1.06 in what was described as frenzied trading, and the French franc dropped to well under a dime, as financial markets anticipated rising U.S. interest rates.

Gold joined in the general retreat, closing off more than $15 an ounce in London at $284.75, according to United Press International. Republic National Bank of New York closed cash gold at $282.75, compared with $295.25 on Friday.

Traders openly talked of the possibility of a 95-cent to 98-cent pound, a French franc worth little more than 8 cents, and a West German mark as low as 25 cents.

The spectacular strength of the dollar, almost unabated since last March, has reinforced protectionist sentiment in the United States, and lately has regenerated a demand by some segments of U.S. industry and agriculture for an import surcharge to offset the effect of the dollar on trade balances.

The import surcharge idea also is being sold as a way of generating revenue to bring down the budget deficit.

The dollar's latest spurt, triggered by President Reagan's observation last week that the United States should not attempt to block the dollar's rise, accelerated when traders found no evidence of intervention by central bank authorities. It was the 15th record-setting day out of 17 business days this month, which led one German trader to say: "Every morning when we come in, the previous day's closing price looks cheap."

The dollar was up sharply against the German mark, from 3.3960 Friday to as much as 3.4565 in New York, before settling back to 3.4385. In Paris yesterday, one dollar bought as many as 10.5625 francs, up from 10.3575 francs Friday, and 2 1/2 times its value just a few years ago.

In London, the pound dropped to a record low of $1.0545 from $1.0765 on Friday before gaining slightly to close at $1.0560; it also fell against the mark. In New York, meanwhile, sterling fell to $1.0536, down from $1.0762. There was no substantiation of rumors that the Bank of England, which already had raised interest rates to 14 percent in a fruitless effort to stem the decline earlier in the month, would hike rates another notch if sterling falls below $1.05.

The hard reality is that the overvalued dollar is a bigger problem for large segments of American industry and agriculture than it is for producers abroad.

Despite the affront to national pride caused by a depreciating currencies, and a loss of capital investment potential for expansion at home, Europe has benefited in other ways from the strong dollar. Many European businessmen, racking up profits on exports here, are quite happy with an overvalued U.S. currency.

Almost duplicating Reagan's assessment of reasons for the dollar's strength, a visiting German diplomat said here last week that "the high level of the dollar is a vote of confidence in the United States. It will stay as high as it is, so long as we continue to believe the United States is a strong and safe haven for investment ."

Even if interest rates were to come down, he added, the extraordinary flow of foreign capital investment into the United States is likely to continue. "It's more important for us to have money in America than to make an extra 3 or 4 percent [age points in interest rate yields]," he said.

For political leaders who must reckon with national pride, the situation is different. But on the same day last week that British Prime Minister Margaret Thatcher was in Washington arguing that "the pound is too low," Federal Reserve Board Chairman Paul A. Volcker told Congress that the Fed would not act to make monetary policy any easier. The markets promptly interpreted Volcker's statement as a further assurance of high interest rates, and the dollar gained new strength.

Most agree that a desirable scenario at this point would be a modest, orderly retreat of the dollar that would dampen protectionist pressures.

The big worry expressed on all sides is that the dollar might take a sudden downward turn, and then collapse as market psychology shifts. Jean-Claude Paye, the new secretary-general of the Organization for Economic Cooperation and Development, voiced the fear in a recent speech in Strasbourg, France, "that the dollar could at any moment begin an excessive and hard-to-control decline."

Economist Alan Greenspan says that U.S. banks have contributed to the dollar's rise by liquidating their investments abroad, increasing the demand for dollars by foreigners to pay off their loans. "At some point, the current liquidation of loans will come to a halt, and the demand for dollars will fall. The only question is when, not whether," he says.

No one know where that "point" is. A new survey by the Morgan Guaranty Trust Co. of New York suggests that foreign capital will continue to flow here at a rapid rate, assuring the continuance of a strong dollar. The ultimate test of a further rise in the dollar -- as distinguished from merely a strong dollar -- is whether interest rate spreads will widen.