Sen. James Abourezk, a first-term Democratic liberal and fighter for Indian rights, announced here today that he will not be a candidate for re-election next year.

At a news conference, Abourezk said he would never again seek public office and would devote his time to his family and law practice. He described his decision as a "very personal" one prompted by a desire to fulfill his responsibilities to his family.

The senator, who will be 46 next month, was repeatedly asked if other factors influenced his decision. He said no maintaining that his job required all his waking hours, that he had never considered himself indispensable and that he had never intended to remain in public life indefinitely.

"I have had, to my sorrow, to watch my children grow up from a distance. I have seen my wife and my children endure, in silence, while my work has kept me from fulfilling my responsibilities to my family," the senator said in his statement.

Abourezk's decision opened the way for a spirited contest for his seat next year. The leading Democratic possibility, and one with whom Abourezk will meet Wednesday, is Gov. Richard F. Kneip, 44, Reps. Larry L. Pressler, who will be 35 next month, and James Abdnor, 53, are expected to be Republican contenders. Another possible candidate is state GOP chairman, Leo Thorsness, a former Vietnam Pon, who ran unsuccessfully against Sen. George McGovern in 1974.

South Dakota, once solidly Republican, now has two Democratic senators, two Republican House members, a Democratic governor and a Republican state legislature. Abourezk was elected in 1972 to succeed Sen. Karl Mandt, a conservative Republican.

When Abourezk was asked if he would leave the Senate reluctantly, he replied, "Not really." When one is on the outside he thinks the Senate is the best job in the world, he said, but once in the Senate one realizes that he must sacrifice almost everything else to the demands of the job. He described a senator's work as "truly fulfilling, but personally draining."

Abourezk said he would return to his law practice, with an office in Rapid City and possibily one in Washington. He said, however, that he would not be a lobbyist.

Abourezk is the only senator of Arab ancestry - his origins are Lebanese - and this has been reflected in his sympathy for Arab demands for the return of their territories conquered by Israel. During his five years in the Senate, he has been a liberal maverick, both on foreign and domestic issues.

He frequently held open house in his Washington home for congressional staffers, journalists and fellow lawmakers. The affairs often would turn into night-long bouts of banjo-picking, singing and political conversation.

November to urge Saudi Arabia and neighboring oil producers to hold down the increase in cost of petroleum.

He said today that he told the Arab leaders that a significant price increase would put President Carter "in a corner and cause a political reacton" at the beginning of his term that would be "very damaging."

Abourezk's championing of Indian rights, particularly since the 1973 crisis at Wounded Knee, has weakened him with some of his constituents, observers here believe. The vast majority of Indians in South Dakota, who constitute 5 per cent of the state's population, are on reservations.

Chuck Bellman, South Dakota's Democratic Party chairman, said Abourezk's withdrawal did not surprise him because in recent months the senator had frequently talked about going back to private life.

"Believe me, I would have loved to have him run again, but he told me he wanted to dedicate himself to his family," Bellman said.

A public opinion poll released the night before Abourezk's press conference showed that if the election were held now the senator would be handily defeated by Rep. Pressler, a secend-term Republican with a conservative voting record.