Kurt Waldheim announced his candidacy today for an unprecedented third term as U.N. secretary general, saying it would be "a duty and an honor" to stay in the $137,500-a-year job.

The 62-year-old Austrian was first elected in 1971, and his second five-year term expires at the end of December.

Waldheim faces stiff competition from several Third World candidates, led by Salim A. Salim, the foreign minister of Tanzania. Salim is viewed as the front-runner among challengers because he already has the endorsement of the Organization of African Unity, and he is expected to win support of the 40-nation Islamic Conference.

The secretary general is appointed by the 154-nation General Assembly on the recommendation of the 15-nation Security Council.

Waldheim's chief advantage in the race is that while few of the major nations are enthusiastic about him, none is believed to be unalterably opposed. Thus he may emerge once again--as he did in 1971--as the compromise candidate.

The United States and the Soviet Union have doubts about Salim. His government is too pro-China for the Kremlin, and many Reagan administration officials consider him to be too radical. One or both might use the veto against Salim.

Europeans have held the secretary general post for all but 10 years, when it was held by U Thant of Burma.

At a press conference today, Waldheim dismissed rumors that he might seek only a two-year interim appointment, saying his candidacy is "for a normal full term" of five years