WASHINGTON (AP) _ The State Department on Friday urged Kenya to investigate allegations of police torture and other human-rights abuses.

The comments came as Kenyan President Daniel T. arap Moi continued meetings in Washington with U.S. officials, including Vice President George Bush and Secretary of Defense Caspar W. Weinberger.

State Department spokesman Charles Redman, commenting on a news report about charges that Moi's government was using torture against political dissidents, said the story raises ''serious questions of serious human-rights abuses.''

The Washington Post reported from Nairobi on Friday that two affidavits presented to the attorney general in the African nation charged that police confined naked suspects in dark cells partly filled with water and beat them with whips in order to obtain confessions.

''We're aware of these charges but we can't judge the accuracy of each allegation,'' Redman said.

''We trust the government of Kenya will investigate these most recent allegations, make the findings public and if abuses or inappropriate practices are occuring, that the guilty parties will be punished and the abuses stopped,'' he said.

Moi arrived in Washington Wednesday for a three-day visit to discuss the declining level of U.S. aid and to recruit American investment in Kenya. Human rights was among issues discussed by Moi and President Reagan at a lunch meeting Thursday.

Moi's lunch with Bush was ''warm, informal and friendly,'' a U.S. official said.

At their meeting Friday, Weinberger and Moi discussed security assistance and regional stability, said a Defense Department statement issued at the Pentagon.

The statement said, ''We support Kenya's efforts to remain a stabilizing influence in southwest Asia and the Horn of Africa. And we would like to return to at least our fiscal 1985 and prior-year assistance levels.''