While President Reagan headed for the rarefied atmosphere of the U.S.-Soviet summit conference in Geneva, Vice President Bush flew here today on a down-to-earth political mission aimed at soothing the angry Farm Belt revolt against administration policies.

Bush met privately for more than an hour with leaders of 16 Iowa farm organizations and state officials, hearing firsthand their descriptions of the hardships caused by the deteriorating farm economy and their demands for action by the Reagan administration. Following the meeting, Gov. Terry E. Branstad said Bush "showed that he is genuinely concerned" with the plight of farmers, which the vice president earlier had made clear was the main message he hoped to deliver during his visit here.

Branstad said the farm organization leaders pressed Bush for administration approval of a new farm bill this year and for a "comprehensive restructuring" of the farm credit system to make more credit available to farmers.

Asked if Bush had promised anything, Branstad said, "He listened. We recognize he is not in a position to make promises."

The farm leaders generally appeared satisfied with the chance to speak with Bush but still impatient for action by the administration.

"He promised us nothing," said Dave Ostendorf, head of an organization named Prairie Fire. "He did not say he was going to do anything, which was a little disappointing."

Ostendorf said Bush listened to the farmers, but added, "It depends on what he does with it."

Lyle Scheelhause, coordinator of the Western Iowa Farm Crisis Committee, said he delivered a blunt political warning to Bush, noting that seven Republican senators from the Midwest face reelection next year and that GOP control of the Senate could end if the farm economy does not improve.

"For the first time, we farmers have a little political clout," he said. "We have this power and we are going to use it."

The meeting was arranged by Branstad, who invited Bush to a fund-raising event for Branstad's reelection campaign but insisted that the vice president also meet with the farm group leaders.

At a news conference before the meeting, Bush called his mission to the Midwest "a listening thing" but made clear he was not bearing any promises of new government initiatives to ease the farm crisis.

"I don't come out here with a lot of new programs and easy answers," he said.

Branstad and Sen. Charles E. Grassley (R-Iowa), who also faces reelection next year, have distanced themselves from Reagan over farm issues and appear to be benefiting politically from that tactic. Branstad has been quoted as saying he did not want the president to campaign for him in Iowa. This put Bush in a particularly delicate position today because of the importance Iowa will hold to his hopes of gaining the Republican presidential nomination in 1988.

Asked at the news conference whether he, too, will follow that tactic if the farm economy remains depressed, Bush tied his fortunes to the success of the Reagan administration.

"I'm not going to turn my back on the president for political gain," he said. "We're in this thing together."

But Bush also sought to soothe the anger of Midwestern farmers by repeatedly proclaiming the administration's concern for the plight of farm families. Acknowledging that the administration may have been "a little slow" in demonstrating its concern, Bush said, "I think we have got to demonstrate to people here that the administration cares, I care, the president cares. I'm not sure people here feel that way."

The trip was Bush's first this year to Iowa, a state he carried against Reagan in the 1980 Republican caucuses, briefly propelling him to the forefront of GOP presidential hopefuls that year. It is also a state that Bush's advisers believe he must win in the 1988 nomination race.

En route here, Bush stopped briefly in Minneapolis, where he addressed a fund-raising luncheon and a meeting of the Minnesota Association of Commerce and Industry.

Speaking to the business group, he urged enactment of the Senate-passed version of legislation to force a balanced budget that is now being considered by a House-Senate conference committee.