The Japanese yen slumped to a 30-month low today on the Tokyo foreign exchange market as the American dollar grew stronger on the basis of continued high interest rates in The United States.

Meanwhile, the dollar retreated on other world money markets, and the price of gold eased overseas and in New York.

The yen closed at 256.40 to the dollar, off 2.70 yen for the day. In three days of trading this week it has declined nearly 7 yen to its lowest value against the dollar since October 1977.

Today's decline prompted the governor of the Bank of Japan, Haruo Maekawa, to warn against speculation of an even lower yen but he didn't disclose what, if anything, the central bank will do to turn the tide.

Foreign exchange dealers blamed the slump on a flight of investments into the United States to take advantage of the high interest rates that have risen swiftly as a result of the Carter administration's counter inflation policy.

A trader for one major bank said the announcement that Chase Manhattan was raising its prime interest rate to 19.75 percent apparently accounted for much of today's decline. It convinced investors that interest rates will remain high in the United States for a long time, he said.

The yen's latest fall is putting heavy pressure on the government to follow the American path and raise its own central bank discount rate to push up lending rates here. That would be widely unpopular with Japanese business leaders who already are complaining that the current 9 percent discount rate is too high and may provoke a recession in the latter half of 1980.

The prime interest rate offered by most Japanese banks is 9.25 percent compared with the 19.50 percent rate common in the United States.

"There is now a 10-percentage-point differential in interest rates, and the money is just flowing into the United States," explained one dealer.

This week's decline is the latest part of a long-running stump for the yen which began in December 1978 when the currency was valued at its historic high point of 175.50 to the dollar.

At one point the government had hoped it would stabilize at about 200 or 210 to the dollar, but that benchmark has long since been abandoned, and dealers now talk wistfully of restoring the yen to about 230.

The Bank of Japan intervened in the market today, buying yen to turn the tide, but it doesn't seem willing to expand the foreign exchange reserves that would be needed to prevent a further decline. Dealers predicted a further slide through the 260 mark before the end of this week.

In New York, Mary Tobin of United Press International reported the following.

The dollar's retreat on other money markets came despite further increases in the prime rate by U.S. banks reflecting a sag in Eurodollar interest rates and the long Easter holiday.

Gold eased in Zurich to $500.50 an ounce from Tuesday's close of $503.50, to $501 in London from $503 and to $496 in New York from $503.

The Comex settlement price was $490.80 an ounce compared with $498.50. The Comex closed at 1 p.m.

Silver was the higher, however, trading at $15.15 an ounce on the cash market in late afternoon, representing the price paid for physical delivery in London, compared with $14.50 Tuesday. The settlement price was $14.60 an ounce, up from $14 Tuesday.

Closing European rates with late New York quotes in parentheses:

Frankfurt, 1.9510 marks, down from Tuesday's 1.9650 (1.9560); Zurich, 1.84825. Swiss francs compared with 1.8691 (1.8570); Milan, 907.95 lira, down from 912.05 (905.25); Paris, 4.4875 francs against 4.5375 (4.5150); Brussels, 32.30 Belgian francs compared with 32.705 (31.40); and Amsterdam, 2.1285 guilders, down from 2.1505 (2.1325).

In London the pound edged up to $2.1550 from $2.1425 Tuesday. London dealers said there was no indication of intervention by the Bank of England.