MANAMA, Bahrain--An Iranian speedboat shot up a Saudi Arabian-owned tanker in the Strait of Hormuz yesterday, hours after President Reagan said the U.S. Navy will no longer ignore attacks on noncombatants in the Persian Gulf region.

The speedboat fired rocket-propelled grenades and machine guns at the 37,011-ton Sea Trader in the strait, the southern entrance to the gulf.

An unexploded rocket dangled from the Sea Trader's hull after the attack but fell into the sea before the tanker reached the port of Dubai in the United Arab Emirates.

The Indian captain, B.R. Pagarkar, reported his vessel sustained slight damage and no casualties among the Indian crew.

It was not known whether any U.S. warships were near the Sea Trader during the attack. Navy officials do not disclose warships' movements, but several U.S. frigates and destroyers have been in the southern gulf since last week, when U.S. and Iranian ships skirmished in the area.

Reagan warned Iran in his weekly radio broadcast Saturday that continued attacks on neutral parties, including gulf shipping, "will be very costly to Iran and its people."

On Friday, U.S. officials disclosed in Washington that the Reagan administration was planning to expand the U.S. naval role in the gulf by giving American commaders the right to intervene in Iranian attacks on non-U.S. flag vessels.

Previously, U.S. warships have only been permitted to provide "humanitaran aid" to non-American ships in distress and requesting aid, but not to intercede in armed conflict involving those ships.

Gulf-based shipping executives, speaking on condition of anonymity, said the Sea Trader encountered a flotilla of six armed speedboats as it sailed into the gulf through the strait about 11:30 p.m. EDT Saturday. The tanker, owned by a Saudi firm but flying the Liberian flag, was bound for the Saudi oil port of Ras Tanura.

Pagarkar said five of the speedboats "went in one direction while one appeared to be heading for another tanker, and I thought we'd escaped an attack. But suddenly it veered toward my ship, asking for the master."

The executives quoted him as saying the speedboat opened fire after the Iranians demanded the ship's destination and indicated they intended to board it.

There was nothing to directly link the raid on the Sea Trader to Reagan's comments or to an earlier report that the United States was preparing to adopt a new get-tough policy following last week's skirmishes between Iran and the U.S. Navy. But the attack, the first since two ships were hit Tuesday in the aftermath of a major U.S.-Iranian clash the day before, suggested Iran was determined to show its ability to carry out shipping raids despite its losses.

In the skirmishes April 18, U.S. Navy forces sank or damaged a half-dozen of Iran's armed craft, including two frigates that have regularly operated in the strait and nearby waters.

There have been no reports since April 8 of Iraqi air strikes on Iranian oil tankers, the type of attacks which have provoked Iranian retaliation against neutral vessels.

Iraq's last reported action in the gulf was Friday, when the official Iraqi news agency said Baghdad's forces sunk a small Iranian naval craft. That claim was not confirmed by ndependent sources or Iran, which is fighting a 74-year-old war with Iraq.