The dollar advanced slightly yesterday as the currency markets awaited further news of the economy's strength and digested the dollar's sharp slide earlier this week.

The dollar also was helped by slightly higher interest rates, market analysts said. However, the dollar failed to rise above the magic 3 deutsche mark level in moderate trading, and many economists said that the dollar will continue on a downward trend in coming weeks.

The dollar reached its peak in February when the British pound traded at $1.03. Since then it has fallen 9 percent on a trade-weighted basis and is back to levels it reached in October. Yesterday, the pound closed at $1.2927; the dollar was worth 2.98 marks, 247.58 yen and 9.0957 French francs.

The strong dollar has caused increased imports, reduced exports and resulting record trade deficits. It also is blamed for lower profits for some U.S. firms and a rise in protectionist tendencies in this country. On the other hand, the strong dollar, by making imports relatively cheaper than domestic-made goods, has helped keep inflation at least one percentage point lower than it would have been otherwise, and has contributed to the weakening in oil prices.

A gradual, orderly reversal of the dollar's advance would help increase exports and benefit many domestic firms that compete with imports. But it also would result in slightly higher inflation, increased commodity prices and possibly higher interest rates, as well as further weakenening economic growth.

A rapid decline by the dollar would require higher interest rates to continue attracting foreign capital to continue financing the budget deficits. That could cause a recession.$"It's hard to see what would substan tially reverse" the dollar's decline, said William R. Cline, senior fellow at the Institute for International Economics. "The question is whether we continue to have a stair-step adjustment right on down."

The dollar, which began to drop sharply in mid-March, also declined in March 1984. But that trend ended when interest rates began to rise and confidence in the reelection of President Reagan strengthened, Cline said. Those factors are missing today, Cline said.

"The size of the imbalance is becoming apparent to everyone," Cline continued. The overvalued dollar is evident in the $100 billion-plus current account deficit and a slowdown in domestic production, Cline said.

The dollar's decline so far has had no dramatic impact on the financial markets, said William V. Sullivan, senior vice president of Dean Witter Reynolds Inc. "It takes time and I don't know how to quantify the lags."

"A lot depends on whether this is a real rout of the dollar," Cline said. "If this turns into a rout, interest rates would have to rise sharply for foreign currency to keep coming in" to continue to finance the trade deficit until exports rise.

One factor that could offset the loss of foreign capital could be a reduction in business investment and the subsequent demand for funds, which already is appearing. Foreign capital last year provided one-seventh of gross investment in the United States, Cline said.

Upward pressure on interest rates caused by the flight of foreign capital could choke off the economic recovery, economists said.

A lot depends on other factors, such as what monetary policy the Federal Reserve Board decides to pursue, whether significant reductions are made in the federal budget deficit, and whether economic growth continues to slow, lessening pressures on interest rates and inflation, economists said.

Economists said the decline in the dollar may already have helped the most competitive U.S. firms, and that if the decline continues it will have an effect possibly a year from now on industries that would have difficulty competing regardless of the dollar's level.

However, "a 10 percent drop is not the end of our foreign trade problems," said Robert Ortner, Commerce Department chief economist. At its peak, the dollar was considered to be 30 percent overvalued; so for the U.S. trade deficit to narrow substantially, the dollar would have to drop by about that much.

Benefits for exporters probably will show up in about a year if the dollar continues to decline, Ortner said. For the smokestack industries such as steel, which would need substantial price reductions to help regain lost markets, the dollar's decline may take longer to have an effect, Ortner said.

Sullivan said that a sustained weakening of the dollar could lead to a pickup in commodity prices -- a boon for farmers and others selling commodities, but a bane for continued low inflation.

Commodities, many of which are traded in dollars, became too expensive for foreigners as the purchasing power of other currencies weakened against the dollar. However, as the dollar declines, the costs of agricultural and raw metals products will drop when valued in foreign currencies, increasing demand -- and prices.