The State Department said yesterday that it is conducting an investigation, in tandem with the Justice Department, to determine whether former U.N. secretary general Kurt Waldheim should be barred from the United States because of alleged Nazi ties during World War II.

The State Department's acknowledgment that it is carrying out its own probe of Waldheim's wartime activities came after Justice Department sources revealed Thursday that Neal Sher, head of Justice's Office of Special Investigations, had recommended that Waldheim be placed on the Immigration and Naturalization Service's "watch list" of persons to be denied entry to this country.

State Department spokesman Charles Redman noted that Secretary of State George P. Shultz shares responsibility with Attorney General Edwin Meese III for making a determination about Waldheim. He added that State officials "are investigating and analyzing the available materials."

Justice spokesmen pointed out Thursday that Sher's recommendation is an advisory opinion and has not yet been reviewed or subjected to any conclusions at the "decision-making level." Asked about the status of State's parallel review, Redman said, "I believe the Justice Department spokesmen have indicated the status."

Other State Department officials, while acknowledging that the case has potentially major diplomatic and political implications, said Shultz had given instructions to conduct a careful and thorough review without regard to the fact that Waldheim is a candidate for president of Austria in elections to be held May 4. These officials said that while they could not say when a decision would be made, they knew of no plan within the administration to withhold it until after May 4 in order to avoid charges of U.S. interference in Austria's affairs.

Waldheim's son, Gerhard, who yesterday ended a U.S. visit, issued a statement in response to news of the Sher memo. He reiterated Kurt Waldheim's denials that he had participated in Nazi atrocities and noted that Austria's current president, Rudolf Kirchschlaeger, after examining a secret 1948 U.N. file alleging Waldheim's complicity in the murder of Yugoslav partisans, said Tuesday that he "would not dare to file an indictment in a regular court."

Justice Department sources said Sher, in making his recommendation, relied not only on the information in the U.N. file but on other documents about Waldheim's past unearthed by the World Jewish Congress and on Waldheim's admission that for 40 years he concealed his service as a German officer in the Balkans from 1942 to 1945.

Several present and former Justice Department attorneys said Meese has discretion to reject Sher's recommendation. But, they added, they could not recall any instance where the OSI, responsibile for investigating and prosecuting war crimes, has been turned down on a recommendation that someone be placed on the "watch list" as a suspected war criminal.

They said under the 1952 Immigration and Naturalization Act it is not necessary to have proof of someone's guilt but only grounds for suspecting he is an "undesirable alien." They said under the criteria normally used, the fact that Waldheim is listed as wanted for war crimes in the U.N. files and in a 1948 U.S. Army list, based on the U.N. records, would be regarded as grounds for excluding him.