First the New York congressional delegation wanted the renovated World War II battleship USS Iowa based in New York harbor for the jobs it would generate.

Then it turned out the battleship might carry nuclear-tipped cruise missiles. Peace groups began protesting, and the delegation flinched.

Now a disgusted Defense Secretary Caspar W. Weinberger, to show his displeasure with the zigzagging lawmakers, has deleted $60 million that had been earmarked in next year's budget for development of a naval port on Staten Island, according to Pentagon officials.

The Navy chose New York over Boston and Newport, R.I., as the "home port" for the Iowa and six other ships with the encouragement of New York City officials and members of Congress, who want the work and revenue the ships would bring. But Weinberger became irritated that many in the delegation showed less eagerness for the ships after local peace groups began opposing the new base.

Michael I. Burch, assistant secretary of defense for public affairs, said he cannot comment on the proposed fiscal 1986 budget until President Reagan releases it early next month. But Burch acknowledged Weinberger's impatience with Rep. Joseph P. Addabbo (D-N.Y.), chairman of the House Appropriations subcommittee on defense, and other officials.

That impatience may be all the greater because on larger issues farther from home Addabbo is a leading critic of defense spending and a thorn in Weinberger's side.

"The secretary feels that Addabbo and others who complain about the presence of nuclear warships and nuclear weapons -- that there are a lot of other communities that have begged us for homeporting and would like us to reconsider," Burch said.

The New Yorkers' ambivalence reflects a controversy that has raged in other cities as the Navy disperses its growing fleet according to a policy of "strategic homeporting" that is intended to reduce the Navy's vulnerability in wartime. The San Francisco Board of Supervisors voted, 6 to 5, on Monday to oppose basing the battleship USS Missouri in San Francisco, an action that Mayor Dianne Feinstein deplored as "conditioned by politics, the politics of the antiwar movement."

During environmental-impact hearings this fall in Staten Island, Manhattan and New Jersey, nuclear-freeze advocates strongly opposed basing the Iowa in New York.

Burch said "we want good relations with the community" in New York, but that it is "unreasonable to ask us for assurances" that none of the ships will carry nuclear weapons.

U.S. policy is to never confirm or deny the presence of nuclear weapons on any ship. Experts said it would not be surprising if some of the ships destined for the Staten Island facility -- a cruiser, three destroyers and two frigates in addition to the Iowa -- carried nuclear-tipped Tomahawk cruise missiles.

Eleven members of the New York delegation recently urged the Navy to modify its policy in New York's case and tell the public whether any nuclear weapons will be aboard. Most of the members who signed the letter had previously urged the Navy to choose New York over other East Coast ports.

Addabbo, who could not be reached for comment yesterday, was not one of the signatories, but he requested clarification of Navy policy in a May letter. Adm. James D. Watkins, chief of naval operations, replied that "national policy" precludes confirming or denying the presence of weapons but said ships are periodically inspected "to ensure that they can safely and securely maintain the capability to store and handle all weapons, including nuclear weapons."

The effect of Weinberger's decision, beyond communicating his displeasure, is unclear, since Congress could appropriate $60 million to be spent only in Staten Island. At the least, however, representatives would be forced to commit themselves on the issue, one official said.

A draft environmental-impact statement completed in October estimated that a new base at the Stapleton-Fort Wadsworth complex on Staten Island would generate 4,700 construction jobs during a four-year period, create 900 permanent civilian jobs and indirectly generate 2,600 jobs in ship repair and related areas.

The statement estimated that the city and state of New York would reap about $3 million in taxes each year as a result of the base.