The Israeli government last night reacted with "deep regret and disappointment" to the election of former U.N. secretary general Kurt Waldheim as president of Austria and hinted that the level of diplomatic relations between the two countries would be reconsidered.

Amid persistent reports that Waldheim, as a junior officer in the German Army during World II, was linked to war crimes against Jews and partisan fighters in Greece and Yugoslavia, senior government officials termed the election results a "nightmare" for Jews everywhere, Washington Post correspondent William Claiborne reported.

Elsewhere, Britain's Labor Party as well as American Jewish organizations echoed criticism of Waldheim's decisive victory in the runoff vote, while in Moscow, the Soviet government news agency Tass praised his U.N. record and accused Washington and "Zionist circles" of meddling in the elections, according to news service reports.

In Washington, the White House said it would reserve comment until it received official results, spokesman Peter Roussel said.

In Israel, Foreign Ministry spokesman Avi Pazner said, "Although Waldheim's election did not come as a surprise, we hoped until the last minute that common sense would prevail with the Austrian people and that the election of a man with a past like Waldheim's to the presidency would be prevented."

Pazner said Israeli Prime Minister Shimon Peres and Foreign Minister Yitzhak Shamir would meet Monday to discuss what steps Israel would take in response to Waldheim's election.

Israeli sources said consideration is being given to downgrading Israel's diplomatic representation in Vienna by not replacing the ambassador there after his scheduled departure next month.

However, noting the importance of Austria as a waystation for Soviet Jews immigrating to Israel, other Israeli officials last night advocated caution in Jerusalem's practical application of its anger over the election, Claiborne reported.

In the United States, Elan Steinberg, executive director of the World Jewish Congress, an umbrella group represented in 70 countries, and the organization whose investigations touched off the controversy about Waldheim's past, said U.S. authorities should bar Waldheim from entering the United States.

"That a majority of the Austrian electorate could choose to ignore both Dr. Waldheim's wartime involvement in Nazi operations and his subsequent unbridled deceit about this period represents a truly sad day in Austrian history," Steinberg said in a statement from New York.

Henry Siegman, executive director of the American Jewish Congress, said in a statement that it was "not by what an earlier generation did, but by their own actions and their own choice that Austrians have covered themselves with shame."

In Britain, a spokesman for the opposition Labor Party suggested that the government ban Waldheim.

A more restrained criticism was offered by the president of Israel, Chaim Herzog, who recalled Israel's first prime minister, David Ben-Gurion, as saying, "While we must not forget the past, we must not let the past adversely effect the future of the state of Israel. . . "

Also in New York, Jewish leaders marched up Fifth Avenue in the 22nd annual Salute to Israel Parade and used the occasion to denounce the election. About 50,000 people attended. Mayor Edward Koch said the election "will be Austria's eternal shame," news services reported.