Interest rates continued their remarkable fall yesterday amid signs that Japan and West Germany are about to cut their official lending rates, leaving more room for the Federal Reserve to follow suit without undermining the value of the U.S. dollar.

Yields on long-term government bonds touched 8 percent during the day, a level not seen for more than eight years. As recently as November, the yield was above 10 percent. This decline has meant a 20 percent capital gain for customers who bought such bonds less than four months ago.

Financial-market participants now are so convinced that rates will keep coming down that, in some cases, rates are lower on money lent for six months than for 30 days. Normally rates are higher if the money is committed for a longer period.

The general move toward lower rates should mean a continued drop in rates paid for car and personal loans and mortgages.

Short-term interest rates have not declined in recent months the way long-term rates have, because of Federal Reserve policy. The Fed has not reduced its 7.5 percent discount rate since last spring, effectively putting a floor under most short-term rates.

For the past two days, financial markets have been buffeted by rumors that the four members of the Federal Reserve Board appointed by President Reagan are determined to push rates downward, even if Fed Chairman Paul A. Volcker is opposed, and even if rates are not cut in Japan and Germany.

In recent congressional testimony, which was approved by other members of the seven-person board, Volcker indicated that concern about a possible loss of confidence in the dollar ruled out any significant easing of monetary policy for now. The Fed chairman said such a loss of confidence could make financing the large current U.S. deficit in its foreign transactions impossible without a sharp rise in interest rates.

According to one of the rumors, newly confirmed Fed Governor Manley Johnson told businessmen at a weekend gathering in Puerto Rico that Japan and Germany are expected to cut their official lending rates shortly and, if they do not, the United States will lead the way. Johnson and the other Reagan appointees, who include Vice Chairman Preston Martin and Governors Martha Seger and Wayne Angell, acting as a "gang of four," would force the issue, Johnson said, according to this rumor.

A Federal Reserve spokesman denied the validity of the rumor, saying that Johnson said that he "never said such a thing." Johnson was not available for comment.

The official denial did little to convince some market participants. One money trader for a major Boston bank declared, "The market feels that there is more to the rumors than just smoke. You saw that yesterday when the front end of the yield curve moved for the first time." (A yield curve is a graphical representation of interest rates plotted according to how long the money is committed. The "front end" depicts the shortest maturities, that is, short-term rates.)

The trader said that he had spoken with an economist who heard Johnson make such comments. "That person was very surprised," the trader continued. "He had not heard comments that direct from a Fed official, ever."

An economist with a major New York government securities dealer, who was skeptical that the Reagan appointees would try to challenge Volcker's leadership in this fashion, said that, regardless of the rumor's validity, it had moved rates lower. Moreover, he said, there is evidence that German and Japanese authorities are about to cut their rates to give their economies a boost.

In Germany, the economist noted, the Bundesbank -- that country's central bank -- had intervened in financial markets to provide more cash to the banking system when rates were at 4.3 percent. Previous interventions had been coming at 4.5 percent.

Similarly in Japan, a variety of preliminary moves have been taken by the central bank that normally come before a cut in its lending rate. Economic growth has been slowing in Japan, partly as a rapidly rising yen depresses export orders.