BONN, DEC. 30 -- Leading western European governments want the United States to raise its interest rates to support the dollar if the U.S. currency falls further on world markets, European government sources said today.

European finance ministers, led by British Chancellor of the Exchequer Nigel Lawson, sought unsuccessfully to persuade U.S. Treasury Secretary James A. Baker III to pledge in last week's seven-nation economic policy statement that the United States would be willing to raise interest rates if necessary to prop up the dollar, the government sources said.

Baker refused, because of fears that higher U.S. interest rates would trigger a recession prior to the 1988 election, they said.

The dollar, which dropped to record postwar lows this week, is likely to fall further in January unless the United States raises interest rates or takes other significant policy actions such as trimming its budget deficit, European-based economists and currency traders said.

Higher U.S. interest rates would tend to support the dollar, by making dollar-denominated investments more attractive. But higher rates also raise the costs of borrowing by businesses and individuals, and in today's fragile economy would increase the risk of a recession next year.

The European sources' comments showed that the Dec. 22 statement by the Group of Seven industrial nations, despite its declared purpose of helping to stabilize the dollar, was not sufficient to allay the Europeans' irritation over what one official called Washington's policy of "benign neglect" toward its currency.

The Europeans are unhappy with the dollar's fall because the corresponding increases in their currencies on world markets makes their exports less competitive, hurting vital domestic industries.

"The decisive steps must now come from the United States. There is a confidence gap {over the dollar}," said one West German source, who spoke on condition that he not be identified.

An official of another European country said, "What has emerged is a statement that reaffirms the desire to restore stability in currency exchange rates without any particular, specific commitment from the Americans about how that can be done. The Americans have to resolve how they'll deal with it."

The Group of Seven, or G-7, consists of the United States, Japan, West Germany, France, Italy, Britain and Canada.

The lack of any explicit new U.S. policy pledges in the G-7 statement was the principal reason for this week's fall in the dollar to record lows against the West German mark and the Japanese yen, economists and currency traders said.

The dollar's fall triggered substantial declines in stock prices yesterday and Monday in New York, London and Frankfurt. Both the dollar and stock prices stabilized today, but only after central banks spent more than $2 billion in three days to support the dollar, currency traders said.

The dollar was quoted at 1.595 German marks in New York today, slightly above the 1.594 figure late Tuesday, and at 123.33 yen, down from 123.45 the prior day.

{In Tokyo Thursday, the dollar plunged at the close of the morning trading session, shattering the 123-yen level for the first time despite heavy central bank intervention, The Associated Press reported. The dollar ended the session at 122.55 yen, sharply lower than Wednesday's close of 123.50 yen.}

The outlook for the dollar remains poor in coming weeks unless the G-7 countries patch up their longstanding differences over economic policy, the economists and currency traders said.

"It boils down to a policy gridlock, and this is unfortunate because the dollar will go down if this gridlock continues," said J. Paul Horne, the Paris-based international economist for the investment firm Smith Barney, Harris Upham and Co.

Most economists and traders said that the market was looking specifically for evidence that the United States was committed to support its currency.

"The Europeans and Japanese are getting a little amazed at the intransigence of Washington on the dollar," Christopher Tinker, a London-based economist for the brokerage house Phillips and Drew Securities Ltd., said.

But Tinker and other economists said that underlying economic factors might begin to change in February and March, and help to stabilize the U.S. currency. In particular, these analysts said that they expected that the U.S. trade deficit would begin to narrow.

The Europeans and Japanese have pressed the United States to make additional cuts in its budget deficit, as well as to declare its willingness to raise interest rates to defend the dollar.

The United States, on the other hand, has called on its partners, especially West Germany, to speed up their economies, thus providing stronger markets for U.S. exports.

A West German source said that the United States could raise interest rates by a small amount without triggering a recession.

He and officials in other countries said that recent U.S. economic data indicated that the U.S. economy still was growing despite the Oct. 19 stock market collapse so fears of a U.S. slump appeared overblown.

An official from another European country noted that European central banks have reduced interest rates significantly since the stock market plunge. The European interest rate cuts help buoy the dollar, by making European currencies less attractive, and encourage growth.

"We feel we've done our share in adjusting interest rates. We now feel that the ball is in the Americans' court," he said.

British finance minister Lawson predicted in a radio interview after the G-7 statement was issued that, "in particular, they {the Americans} will sooner or later have to be prepared to raise their interest rates."