The United States yesterday rejected the challenge issued at the United Nations Tuesday by Soviet President Leonid Brezhnev to join in renouncing the first use of nuclear weapons.

A statement issued by spokesman Dean Fischer at the State Department called the Soviet no-first-use pledge "unverifiable and unenforceable," and "not an effective way to reduce the danger of nuclear war."

The Soviet promise not to be the first to use nuclear weapons in conflicts with other nations was announced in a speech to the U.N. Special Session on Disarmament by Foreign Minister Andrei A. Gromyko. A letter from Brezhnev, read by Gromyko, went on to say that "the world has the right to expect that the decision of the Soviet Union will be followed by reciprocal steps on the part of the other nuclear states."

President Reagan, who is to address the special U.N. session today, is not expected to respond in that forum to the Brezhnev challenge. It was decided, instead, to deal with the matter in yesterday's brief State Department statement.

"A simple pledge gives no assurance that an aggressor would not in fact resort to the first use of nuclear weapons during a conflict or crisis," the statement said.

Quoting from an April 6 speech by Secretary of State Alexander M. Haig Jr., the State Department said that, in view of the large Soviet advantage in conventional military forces in Europe, a no-first-use pledge from the Atlantic alliance would be "tantamount to making Europe safe for conventional aggression."

U.S. efforts to deter war by maintaining large-scale forces and to reduce those forces through negotiations would be "more effective and credible" than a no-first-use pledge as a means of reducing the danger of war, the statement said.