The House Republican leadership yesterday joined the White House and some members of the Senate in strongly urging the Federal Reserve not to tighten monetary policy or raise interest rates.

In a letter to Fed Chairman Paul A. Volcker, the GOP leaders warned, "We, and a great many of our colleagues, would look with extreme disfavor upon any increase in the discount or federal funds rates at this time."

Any such action would be "ill-advised" and "unnecessary" at this time, said the letter, which was signed by Minority Leader Robert H. Michel of Illinois, Whip Trent Lott of Mississippi and five other members of the leadership group.

Meanwhile, House Speaker Thomas J. (Tip) O'Neill of Massachusetts also complained about rising interest rates, but he blamed them on a failure by President Reagan to provide the necessary leadership to reduce federal budget deficits. O'Neill did not mention the Federal Reserve.

The Fed's policymaking group, the Federal Open Market Committee, completed a two-day meeting yesterday at which it decided on what monetary policy course to follow in coming months. As usual, no announcement of its decisions was made.

Volcker will testify at his confirmation hearing for a second term this morning before the Senate Banking, Housing and Urban Affairs Committee. He is expected to be asked about the FOMC decisions.

Last week it was reported that the FOMC intended to tighten credit conditions in order to slow growth of the money supply, which by some measures has been well above the central bank's target range for most of this year. Federal Reserve officials said they believe such a step is necessary because of a combination of rapid economic growth and the continued prospect of large, stimulative federal budget deficits.

Since there is a lag before changes in the money supply affect both the level of economic activity and prices, the Fed officials said they want to slow money growth now in order to keep the economy from getting out of hand later in ways that could rekindle inflation.

The House Republican leaders explictly rejected such arguments in their letter. Reiterating the views of Rep. Jack Kemp of New York, one of the signers, the letter said, "Concern has focused on the growth of M1 or on the strength of the economic recovery as supposed harbingers of renewed inflation. But we must reject the notion that too much economic growth is the cause of inflation . . . Moreover, as you know from the Federal Reserve's recent experience with money supply targets, the M1 definition of the money supply, taken by itself, has been quite misleading as an indicator of monetary policy."

The M1 measure of money, which has been far above the upper limit of the Fed's target range, includes currency in circulation, checking deposits at financial institutions and travelers checks.

The letter also cautioned, "The jobs and hopes of Americans must not be dashed out of abstract concern for one arbitrary measure of the money supply. The current recovery has barely returned the economy in real terms to its 1979 level, and industrial production remains far below it. The recovery must not be needlessly jeopardized by an unnecessary rise in interest rates."

O'Neill's statement noted that last month he warned the American Stock Exchange that "President Reagan's continued failure to reduce federal deficits would trigger higher interest rates. Today that prediction has become a reality. Interest rates are up. Mortgage costs are up. The major forecasters are predicting even higher rates in the months ahead.

"To me," the speaker continued, "this is the big political--as well as economic--story of 1983 . . . The president's lack of leadership in the economy remains the key issue of 1984."