The Reagan administration emerged from its first meeting with the new leader of the Soviet Union, Yuri V. Andropov, with agreement by both sides to continue high-level contacts, a senior State Department official said yesterday.

The meeting with Andropov was a "useful" session, the official said. "We now have a channel to him."

Vice President Bush and Secretary of State George P. Shultz met with Andropov for half an hour Monday after the funeral of Soviet President Leonid I. Brezhnev.

"The idea of a summit meeting was not raised," the official said, "but the suggestion of continuing the dialogue between Shultz and Soviet Foreign Minister Andrei Gromyko" received support. It was not clear who raised the possibility of more meetings between Shultz and Gromyko.

Shultz and Gromyko met for more than seven hours during the opening days of the U.N. General Assembly in late September and early October. The apparent endorsement for further meetings between them is the first specific sign that both the new Soviet leadership and the Reagan administration are willing to probe each other's intentions at a senior level.

Andropov was a shadowy figure in the Kremlin hierarchy for a decade and a half, during which he headed the KGB, and U.S. officials admit to having had virtually no firsthand contact with him. Last weekend was the first real opportunity U.S. officials have had to observe Andropov and deal with him directly.

"On all occasions when U.S. officials saw him we came away with a feeling that this is not a diffident sort of fellow. There was an impression of a man very much in control, of a man able to make decisions. He came on strong," the official said.

He also said that both Andropov and Gromyko were at the meeting with Bush and Shultz, but that Andropov did most of the talking for the Soviets.

Shultz, following a report to President Reagan yesterday morning on the talks, said that he and Bush had emphasized a willingness to work for improved relations but had made it clear that the United States was not prepared to shift its policy of approaching Moscow from a posture of military strength.

Shultz said U.S. policy toward the Soviet Union is based on four points: "a realistic appraisal of what is going on; on the strength of our military capacity and our willpower; a willingness to solve problems; with a conviction, number four, that things can be better if problems are solved."

"We've tried to put some emphasis on point three, but we must remember that there are . . . four parts," Shultz said.

The senior department official emphasized yesterday that Sunday's meeting was not a "breakthrough" in itself and that the substance of the discussions with Andropov had been a clear expression by both sides that each is committed to a program of military strength but, having said that, each is willing to talk to the other.

Bush and Shultz attended Brezhnev's funeral after President Reagan reportedly rejected advice that he attend as a signal to the new Soviet leadership of a U.S. desire to thaw relations between the superpowers.

In their public statements in Moscow, both Bush and Shultz emphasized U.S. willingness to improve ties with the Soviets.

Bush yesterday resumed an African tour he had interrupted to go to Moscow.