The yen slumped to a 26-month low today on the Tokyo foreign exchange market as the American dollar gathered strength on the basis of continued high U.S. interest rates, turbulence in the Middle East and a flagging Japanese economy.

The yen closed at 250.55 to the dollar in moderately brisk trading, its lowest point since April 22, 1980 and 3.15 off Friday's market close. The Bank of Japan tried to stave off the decline, private banking sources said, by selling more than $200 million into the market, but the intervention appeared to have little effect.

Now that the currency has snapped the 250-yen-to-the-dollar level, a closely watched "pyschological" barrier here, foreign exchange dealers predicted that the yen was likely to hit 260 yen to the dollar within the next week or so before breaking its own fall.

The political uncertainty touched off by the Israeli-Lebanese conflict helped spark a speculative dollar-buying spree among Japanese and foreign traders, foreign exchange dealers said. Japan relies overwhelmingly on the Middle East for its oil supplies, and any serious unrest there tends to rattle the yen.

But market observers blamed the slump primarily on a flight of investments into the United States to reap the benefits of higher interest rates there. The consensus in the market here recently has been that U.S. interest rates would decline following the passage by Congress of the Reagan administration's budget proposal.

"The mood of the market now," one Japanese banker said, "is that there is no hope for U.S. interest rates to come down significantly in the next two to three months and that the dollar will remain strong despite the passage of the budget. People are starting to act on that basis, even those who firmly believed the yen was bound to get stronger."

The prime interest rate offered now by most Japanese banks is 5.75 percent, compared to 16.5 percent common in the United States. "With that kind of gap in interest rates," said one American banker based in Tokyo, "the yen is certainly not likely to get any stronger" and may be headed for a prolonged bout of weakness.

The value of the yen has continued to fall despite a large-scale dollar-dumping campaign by Japanese monetary authorities, which, according to one private banking source, has seen the central bank use some $3 billion to buy up yen since the 1982 market opened in January. The Bank of Japan, as a matter of policy, does not disclose the extent of its intervention.

Among those signs was the government's announcement last week that Japan's economy had registered a real growth rate of 2.7 percent in the fiscal year ended March 31, far below its original forecast of 5.3 percent. Private economists predicted that Tokyo is also likely to undershoot its target for growth in the current fiscal year of 5.2 percent.

Japanese observers worry that the low yen will boost Japan's trade surpluses and help further aggravate Japan's critics in the United States and Europe who charge that the country is already selling far too much and buying too little.