SANTA BARBARA, CALIF., AUG. 15 -- President Reagan warned Iran today that the United States will not "permit extremists to set the agenda or coerce their neighbors" in the Persian Gulf.

"We have to show that efforts of intimidation, like Iranian threats against Kuwait and other nonbelligerent states in the gulf, do not work," Reagan said in his weekly radio address. "We're a tolerant people, but we do not bow to intimidation, and we've consistently throughout our history been willing to defend ourselves. Our tolerance should not be mistaken for a lack of resolve."

Administration officials said that the statement was intended as a warning to Iran that the United States intends to maintain its commitment to free navigation in the gulf and is prepared to respond to terrorism or other acts of intimidation.

Robert E. Lamb, chief of the State Department's bureau of diplomatic security, said Friday in Washington that Iranian officials, some of them accredited diplomats, had been casing U.S. embassies to determine which are especially vulnerable to attack.

Officials, speaking on condition they not be identified, said the United States also has received warnings from other countries of stepped-up Iranian planning for terrorist activity, especially in the Middle East. They declined to discuss specifics of this information, which they said came from intelligence sources.

On Friday, the United Arab Emirates newspaper Al Khaleej warned that Iran might deploy small "booby-trapped boats operated by remote control" in international waters outside the Strait of Hormuz. U.S. officials said they take this possibility seriously.

Reagan's radio speech reiterated U.S. support for "diplomatic efforts in the United Nations and elsewhere to defuse tensions and pursue a prompt negotiated settlement to the Iran-Iraq war," now in its seventh year. The president also said that "we will press our efforts to resolve the Arab-Israeli conflict, recognizing that stalemate will strengthen those very forces most opposed to peace."

The speech was broadcast from a studio at Reagan's ranch, Rancho del Cielo, 20 miles northwest of here. Reagan is spending most of a 25-day California vacation at the ranch, where he went riding later in the day with his wife, Nancy.

White House spokesman Marlin Fitzwater said Reagan will fly to Los Angeles on Aug. 26 for a midday speech on U.S.-Soviet relations. It is expected to focus on prospects for arms-control agreements.

In his radio address today the president touched on most of the themes that were the subject of a nationally televised speech from the Oval Office last Wednesday.

Speaking of the hearings into the Iran-contra scandal, the president said, "The issues involved have been examined from every angle and in every light. The mistakes that were made have been dealt with. Now it's time for Americans to come together and move our nation forward."

Reagan called on Congress to "pass a responsible budget that is credible and enforceable" and reaffirmed support for his controversial Supreme Court nomination.

"My nomination of Judge Robert Bork to the Supreme Court comes at the top of our nation's domestic agenda," Reagan said. "Judge Bork is a . . . man of great intellect and broad experience. Like me, Judge Bork believes in judicial restraint, that courts should not interpret the law and that judges should not substitute their own personal views for those of legislators whose responsibility it is to make the laws."