The falling dollar is driving up the price of foreign products in the United States, a sign that imports are begining to lose their price advantage over domestic goods, the Labor Department's import and export price index shows.

The change is most pronounced in products from Japan and West Germany, where the dollar has fallen the most in the past 14 months, according to the report, which was released last week. But the price of products -- especially clothing -- from newly industrialized countries of the Far East, whose currencies have remained stable, has not increased.

Bill Alterman, chief of the Bureau of Labor Statistics' international price index, said import prices began rising in mid-1985 after years of declines. "It picked up speed in the fourth quarter of last year and accelerated further in the first quarter of 1986," he said.

In all, the average price of imported products -- excluding fuel oils -- increased 6.6 percent from March 1985, when the dollar reached its peak, to last March. This increase in the price of imports followed a 3.9 percent drop in the previous 12-month period, from March 1984 to March 1985.

The dollar has dropped more than 35 percent against the Japanese yen in the past 14 months, falling to a record low of 165 yen yesterday. At its peak, the dollar was valued at 265 yen.

Overall, against a basket of currencies, the Labor Department said the dollar dropped 20.4 percent since March 1985. It dropped 6.1 percent from December 1985 to last March.

A lower-valued dollar makes foreign goods more expensive in the United States and lowers the price of U.S. products in other countries. The currency realignment is expected to help ease the U.S. trade deficit, which soared to a record $148.5 billion last year and is expected to remain at that level this year. Reagan administration officials have cautioned that the full effects of the falling dollar will not be reflected in the trade balances until the last half of the year.

Jerry Jasinowski, chief economist of the National Association of Manufacturers, said the increased price of imports should make American products more competitive, but said a 6 percent rise is not enough.

The import price increases for the first three months of this year increased in all major categories except petroleum products, which have been tumbling with the world oil glut. The oil price index hit its lowest level since June 1979 in the quarter that ended in March.

The category of crude materials registered its first price increase in two years last March, rising 3.8 percent after a 7.8 percent decline last year. This category includes crude rubber, up 7.7 percent; metal ores and scrap, up 6.8 percent; and wood, up 4.9 percent.

Some of the largest increases came in capital goods, where U.S. makers have been especially hard hit by competition from Europe and Japan. Prices of general, specialized and metal-working machines increased by more than 16 percent.

The price of wines, largely from Europe, increased by 3.2 percent, the largest quarterly increase in four years. Prices of medical supplies and pharmaceuticals, largely from Europe, jumped 6.4 percent.

Japanese camera makers increased their prices 16.2 percent over the past year after four straight years of declines. Japanese cars were up 4.8 percent in the first quarter of 1986, registering their largest price increase since 1981 other than for major year-end model changes. Tape decks and video cassette recorders, produced largely in Japan, ended five straight quarters of price declines. In the past two quarters, the prices increased 3.2 percent and 5.6 percent.

The price of stainless steel flatware went up 17.3 percent over the past year compared with a 7.6 percent drop in the previous 12 months.