Spurred by a grass-roots disarmament movement that has gained strength across the nation in recent months, 17 senators and 115 House members yesterday introduced bipartisan resolutions in Congress calling on the United States and the Soviet Union to agree to a nuclear weapons freeze, followed by major reductions on both sides.

At a news conference at American University, Sen. Mark O. Hatfield (R-Ore.), a chief sponsor of the resolution, described his visit to Hiroshima after the bomb was dropped in August, 1945. He said he observed "nothing but a mass of rubble and a stench of rotting human life." Today, he said, "we have the equivalent of 1 million Hiroshima bombs. We have the capacity to destroy civilization as we see it."

Hatfield and others say the opportunity for negotiations is unique now because the United States and the Soviet Union have a "rough equivalency" in nuclear arms.

"Will the time ever be more right?" asked Jonathan B. Bingham (D-N.Y.), a cosponsor of the resolution in the House. "Will the Russians stand still while we build the MX missile, the B1 bomber and the Trident submarine?"

But Secretary of State Alexander M. Haig Jr. said a nuclear freeze would harm national defense and President Reagan's strategy for reducing the level of nuclear arms around the world. He said a freeze would have the effect of freezing a Soviet advantage in nuclear weapons in Europe that may be as high as 6 to 1 over the West.

"It's not only bad defense and security policy, it's bad arms control policy as well," Haig said, adding that a freeze would take away any inducement for the Soviets to reduce their level of arms.

In New Hampshire Tuesday, persons attending 21 town meetings endorsed a freeze on nuclear weapons, while majorities at four town meetings voted against it. Similar endorsements were given at 159 of 180 town meetings in Vermont last month. Freeze resolutions have passed in the Connecticut, Massachusetts and Oregon legislatures, and in the Wisconsin, Kansas and New York assemblies.

According to Randall Forsberg, director of the Institute for Defense and Disarmament Studies in Brookline, Mass., more than a million people have signed freeze-related petitions.

Referendums have passed in parts of Massachusetts and Colorado, and referendum initiatives have been launched in California, Michigan, New Jersey and Delaware. Forsberg said that groups supporting a freeze are active in two-thirds of the congressional districts.

The congressional resolution on a nuclear arms freeze--cosponsored in the Senate by Edward M. Kennedy (D-Mass.) and in the House by Edward J. Markey (D-Mass.) and Silvio O. Conte (R-Mass.)--expresses the desire of Congress to return to the arms-control bargaining table, but would not unilaterally affect the production of arms.

It states that "as an immediate strategic arms-control objective, the United States and the Soviet Union should: (a) pursue a complete halt to the nuclear arms race; (b) decide when and how to achieve a mutual and verifiable freeze on the testing, production and further deployment of nuclear warheads, missiles and other delivery systems, and (c) give special attention to destabilizing weapons whose deployment would make such a freeze more difficult to achieve."

The resolution adds that "the U.S. and the Soviet Union should pursue major, mutual and verifiable reductions in nuclear warheads, missiles and other delivery systems, through annual percentages or equally effective means, in a manner that enhances stability."

Among those endorsing the resolution at yesterday's news conference were Paul Warnke, a former director of the Arms Control and Disarmament Agency; former presidential adviser Averell Harriman; Bishop James Armstrong, president of the National Council of Churches; Rabbi Alexander M. Schindler, president of the Union of American Hebrew Congregations, and the Rev. Timothy Healy, president of Georgetown University.

In a related development, President Reagan informed Congress yesterday that U.S. cooperation with the European Atomic Energy Community is essential and should continue "to counter the threat of nuclear explosives proliferation."

In a letter to Senate and House leaders, Reagan said he was signing an executive order to continue the agreement with the community, known as "Euratom," for another year.