Soviet Foreign Minister Andrei Gromyko, in his first meeting with an American official since the talks in Geneva, told Sen. Gary Hart (D-Colo.) today that he hopes U.S. negotiators will move directly to "concrete proposals" when the two sides resume arms negotiations.

In a brief interview outside the Kremlin, where he spent two hours with Gromyko, Hart said the Soviet foreign minister stressed that the arms talks should begin "sooner better than later, . . . but not if sooner leads to generalities."

Hart, who unsuccessfully sought the Democratic presidential nomination last year, reportedly is positioning himself for another try in 1988. His reception here by Gromyko and other Soviet officials indicates that the Soviets are interested in his future prospects.

A Hart aide described the atmosphere at today's meeting as "frank, businesslike and friendly." He said the meeting had been expected to last 30 to 45 minutes.

Hart, a member of the Armed Services Committee, said much of his conversation with Gromyko centered on the coming arms negotiations agreed upon by Gromyko and Secretary of State George P. Shultz in Geneva earlier this month.

Hart said Gromyko reiterated the Soviet position "in terms virtually identical" to statements made in an interview on Soviet television Sunday.

The Soviets have made clear that their top priority in the talks is to halt the U.S. development of space-based weapons. According to Hart, Gromyko did not repeat his statement made on Soviet television that an American failure to negotiate in good faith over the space weapons issue would "blow up" the talks.

Neither the date nor the site for the talks has been set, and Gromyko told Hart that he hoped the dialogue over timing and location does not go on "overly long," and that both sides should be ready with specific proposals.

Hart said the conversation also touched on issues of compliance in arms control and on human rights. He said he stressed U.S. concerns about human rights abuses in the Soviet Union, and raised specific cases involving families of Colorado residents.

"I was more concerned with individuals than with debating generalities," he said. While objecting to outside interference in internal Soviet affairs, Hart said, Gromyko said his staff would investigate the specific cases. Hart gave no details about the cases.

Human rights also were stressed in meetings between Soviet officials and a group of U.S. congressmen here this week on a parliamentary exchange.

Headed by Rep. Tom Lantos (D-Calif.), members of the group said they told Soviet officials that the United States was not ready to accept "detente without a human face."

"The climate has to be right for arms control," Lantos told reporters this week.

Hart, winding up a 10-day European tour, is here as a guest of the Supreme Soviet, or parliament, and the U.S.A. and Canada Institute.

He was a lunch guest of Supreme Soviet officials in the Kremlin today and has meetings Friday with director Georgy Arbatov and other members of the institute.

Hart, who is accompanied by his wife, two children and two aides, will visit Leningrad before leaving the Soviet Union.