The Navy's plan to build a $300 million base on Staten Island for the USS Iowa and six support ships has run into opposition here, forcing the issue onto the November ballot.

Critics say the ships, which are capable of carrying nuclear weapons, would make the nation's largest city a more tempting target for a Soviet attack and would endanger millions of lives if one of the ships were to be involved in an accident in New York Harbor.

The home-port issue is the first referendum in 19 years to be placed on the ballot here as a result of a grass-roots campaign. More than 111,950 signatures, gathered by volunteers from the Mobilization for Survival, an antinuclear group, and other citizens' organizations, were ruled valid in the state Supreme Court last week.

If the referendum passes, it would be a major public relations setback for the Reagan administration's plan to build political support for an expanded fleet by dispersing new ships around the country. "We'd be the laughingstock," said Sen. Alfonse M. D'Amato (R-N.Y.).

Opposition has also surfaced to the Navy's plans to base the battleship USS Missouri and six other ships in San Francisco. That city's board of supervisors voted 6 to 5 against accepting the ships last spring, but Mayor Dianne Feinstein vetoed the resolution. A poll showed city residents were evenly split.

New York's would be the country's second referendum on home-porting. Another ballot initiative seeking to block the ships failed by 2 to 1 last year in Everett, Wash. There the Navy plans to base the nuclear-powered aircraft carrier USS Nimitz and 12 other ships.

Navy Secretary John F. Lehman Jr. has called the New York controversy "a healthy debate," expressing confidence that voters will approve the home port. Regardless of the outcome, the Pentagon would have the legal authority to condemn the land and build the base, but it is questionable whether it would use it, according to home-port advocates.

D'Amato, Sen. Daniel Patrick Moynihan (D-N.Y.) and other members of New York's congressional delegation called a news conference Thursday to urge New Yorkers to reject the referendum. "Have you ever opened up a locker of warheads?" Moynihan inquired. "They just look like five-inch shells . . . . They are inert. They are perfectly safe things . . . . It takes a hell of a lot of organizing to get a nuclear reaction, I assure you."

City officials, who had told the Navy they would provide free land and $15 million worth of port improvements, will go to court Monday to try to bar the referendum from the ballot on constitutional grounds. A vote would interfere with the federal government's right to provide for the national defense, they argue.

Mayor Edward I. Koch has declared that rejection of the home port, "would be the eternal shame of the city of New York . . . . I believe that love of country is involved here."

As for the possibility of an accident, Koch said, "We are part of the United States. Are the lives of people in Hampton Roads, Va., and San Diego less valuable than people are in New York?"

In the cavernous sanctuary of the Good Shepherd Church on Manhattan's Upper West Side, some 80 neighborhood residents gathered last week to sing antinuclear songs and applaud speeches by home-port opponents, including City Council President Carol Bellamy.

"The most patriotic thing" would be to vote against a home port, she said, because "the greatest threat to national security is the escalation of the arms race."

Thomas DeLuca, a former political science professor who heads the local chapter of Mobilization for Survival, said he thought "it was a joke" when he heard of the plan to put the ships here. "New York City is the most densely populated city in the country. If an accident happened here, it would be catastrophic," he said.

Basing the ships in New York "is not necessary for national security," he said. "It's about politics. The Navy wants to give each congressional delegation a couple of ships while it's asking them to remember to vote the right way" on military spending bills.

The referendum would amend the City Charter to "restrict the powers of the Board of Estimate to facilitate the development of any military facility, any component of which is designed to carry or store nuclear weapons."

Thus, a "yes" vote is a vote against the Navy, a confusing factor that troubles home-port supporters. A low turnout is likely, since Koch, having won the Democratic mayoral primary, is considered a shoo-in in the general election. Thus, even a limited turnout of antinuclear voters could be significant.

Hearings and appeals on both the validity of the petition signatures and the constitutional question could ricochet from court to court over the 2 1/2 weeks before the election. "It's hard to understand why there is a constitutional issue," said Anne E. Simon, an attorney with the Center for Constitutional Rights, a civil rights group that is representing home-port opponents.

"This referendum does not tell the U.S. Navy it can't come to Staten Island. It only says that the Board of Estimate can't volunteer money or land." The Board of Estimate is a governing body that includes the mayor, the City Council president and representatives of the five boroughs.

City attorneys, however, contend that the measure could prevent the city from rebuilding roads, hooking Navy facilities to water and sewer lines and providing other services. "It would require the Board of Estimate to be uncooperative to such an extent as to be an unconstitutional interference," according to a city legal brief.

The Navy will not publicly state whether the ships will carry weapons into the harbor, but many supporters acknowledge that they probably will.

D'Amato quoted a General Accounting Office report estimating that "the possibility of an accidental nuclear explosion while transporting or storing nuclear weapons is so remote as to be virtually nonexistent."

Should an accident occur, however, GAO reported that a seriously damaged nuclear warhead could emit a cigar-shaped cloud of radioactive plutonium that would stretch for about 28 miles from the site.

The issue has also become a point of contention in the New Jersey governor's race, with Democratic candidate Peter Shapiro opposing the facility "because of the potential for accidents." Gov. Thomas H. Kean (R) supports the base, noting, "We've been asking in this part of the country for more military expenditures. We've been asking for more jobs to be created."

However, Kean also expressed concern about the lack of information from the Navy as to what hazardous materials might be located at Earle Naval Weapons Station in Colts Neck, N.J., where some of the ships' weapons may be unloaded.

According to Navy figures, the base, with 3,500 Navy personnel and a payroll of $70 million a year, will generate about 900 new civilian jobs.