CEDAR RAPIDS, IOWA, OCT. 13 -- Vice President Bush, insisting that the administration would not make a "dumb deal" with the Soviet Union, challenged other Republican presidential candidates today to support the prospective agreement on eliminating medium-range and shorter-range nuclear missiles in Europe.

On the first day after formally launching his campaign for the 1988 Republican presidential nomination, Bush sought to exploit what strategists say is one of his stronger hands: his association with the first major arms control agreement of the Ronald Reagan years.

Bush's readiness to make the treaty an issue suggests that the Republican campaign will focus at least in part on Soviet arms control agreements, as did the campaigns of 1976 and 1980 when Reagan had been a harsh critic of detente and treaties reached by Presidents Richard M. Nixon, Gerald R. Ford and Jimmy Carter. In part because of President Reagan's abiding anticommunism, some political analysts suggest it will be difficult for today's Republicans to make a convincing case against his first arms control deal.

Bush is the only unqualified advocate of the agreement among Republican presidential contenders. His chief rival, Senate Minority Leader Robert J. Dole (R-Kan.), has said he has concerns about verification, but is expected to back a treaty. Rep. Jack Kemp (R-N.Y.), former Delaware governor Pierre S. (Pete) du Pont IV, former television evangelist Marion G. (Pat) Robertson and former secretary of state Alexander M. Haig Jr. have all expressed objections to the treaty.

Final details of the agreement are expected to be worked out next week in Moscow by Secretary of State George P. Shultz and Soviet officials.

Some critics have said that the agreement would leave Western Europe exposed to a large Soviet and Warsaw Pact numerical advantage in conventional forces. Others have expressed concern that Reagan is too hastily pursuing a deal out of concern for his legacy that would disengage the United States from its longstanding commitment to the defense of Europe. Recent doubts about the wisdom of the pact have been voiced by former secretary of state Henry A. Kissinger and former United Nations ambassador Jeane J. Kirkpatrick.

"This president isn't going to enter into a dumb agreement," Bush told reporters today. "We're not going to do a dumb deal."

Later, in a speech at the Linn Mar High School, Bush defended the prospective treaty as "hard-headed, verifiable, and in the best interests of our national security and God knows it's in the best interest of peace." In a series of appearances in Chicago and Iowa, Bush said he wanted to "press my opponents in this race to say if they're for it or against it."

Bush also grappled with repeated questions about his political identity after he delivered an announcement speech Monday sounding traditional Republican moderate themes and implicitly criticizing the Reagan years. Today, he insisted that he remains a Reagan loyalist. "I'm basically conservative" and "always have been," he said this morning in an interview with Cable News Network, adding that he "voted that way in Congress" nearly 20 years ago.

Bush said he has had differences with Reagan over the years, but reiterated that he would not elaborate on them because it would "play into the hands of those six Democratic candidates running all over Iowa all the time."

Continuing to portray his campaign as being closer to the voters, Bush today posed for photographs greeting subway riders in Chicago and later worked a line of cheering high school students here, a scene filmed by his campaign for use in commercials.