The dollar plunged yesterday to its lowest level against the Japanese yen since World War II, and President Reagan said he will press major U.S trading partners next month to consider how currencies can be stabilized.

During an interview with news agencies before his trip to the seven-nation economic summit in Tokyo May 4 to 6, Reagan said he wants to "quit having this volatility and ups and downs" in currency movements.

The dollar closed in Japan yesterday at 171.90 yen, down from 173.15 yen at the opening of trading. In New York, the dollar closed at 171.15 yen, down from 172.45 on Friday.

The dollar declined against other currencies, too. It fell in New York to 2.1935 West German marks from 2.2190 on Friday, and to 7.0025 French francs from 7.0765.

The dollar has fallen 35 percent against the yen since reaching 262.55 yen in February 1985. It has fallen almost 20 percent since Sept. 22, when the United States and four of its major trading partners announced coordinated efforts to push the dollar down.

When asked whether the dollar should fall further against the yen, Reagan said, "I prefer to put it that the yen has risen in value in comparison to the dollar.

"This figure -- I don't know whether it has to change or not -- I believe this is supposed to be the highest value of the yen against the American dollar that we've ever known, certainly . . . in the half century since World War II," Reagan added later.

Japan's finance minister, Noboru Takeshita, also said yesterday that joint action should be taken to stabilize exchange rates.

The dollar attempted a comeback in New York, but fell abruptly on misstatements of President Reagan's remarks on the dollar and yen relationship, foreign currency traders said.

Currency traders said they were beginning to get nervous about the dollar's decline and that it may be difficult to stop its slide. The Bank of Japan yesterday reportedly bought between 1 billion and 1.5 billion dollars in an attempt to prop up the dollar, but it continued to fall.

On Friday, the Federal Reserve Board lowered the discount rate from 7 to 6.5 percent in an effort to stimulate the economy. The Fed coordinated the move with other trading partners to prevent a run on the dollar. On Saturday, as agreed with the Fed, Japan lowered its discount rate from 4 to 3.5 percent.

"The trading community is bearish on the dollar," Snow said. "The dollar could well go to 165 yen. That probably would not be out of range. That's probably the first target the Treasury will feel comfortable with. Along the way, there would be Japanese interventon to support the dollar, both verbal and in the sense of buying the dollar."

Allen Sinai, chief economist for Shearson Lehman Bros., said that as long as the yen is appreciating, yen-denominated assets probably will be considered of higher value than dollar assets and thus will be more attractive to investors and will help cut the dollar's value.

Sinai also said that the rate of economic growth is expected to be faster in Japan than in the United States. Japan also is expected to benefit more from the decline in oil prices than most other countries because it is more dependent on oil imports. These factors will help to make the yen more attractive against the dollar, Sinai said.