MANAMA, Bahrain (AP) _ Fires flared today on the missile-ravaged USS Stark, interrupting its progress toward port, and the Pentagon raised the death toll in the Iraqi missile attack to 37.

Marine salvage executives said the frigate was about 60 miles northeast of Bahrain this morning, alternately halting so crews could fight the fires and then resuming its slow journey under tow.

The Stark has traveled only about 25 miles since being hit Sunday night by one or two Iraqi Exocet missiles that punched a hole in the port side and ignited intense fires.

In Washington, Pentagon spokesman Cmdr. Robert Prucha said today 37 crew members were killed, up from the previous figure of 28. He said 22 were positively identified and 15 were missing and presumed dead. In addition, 21 sailors in the 182-member crew were injured.

''The inside of the Stark got so hot that the aluminum melted,'' said one salvage executive, speaking on condition of anonymity. ''During the fire it was like the inside of a boiler'' with temperatures reaching 1,832 degrees, he said.

''It has been extremely hazardous to tow the Stark, and she cannot move under her own power,'' another executive said. ''The alloy of the stricken section is very hot and keeps reigniting fire. The crew keep dealing with rebursts and the ship meanwhile comes to a standstill.''

The executives said the tugboat Smit Rangoon sprayed foam and water on the ship in an effort to cool it.

Iraqi President Saddam Hussein, in a letter to the State Department, expressed ''deepest regret'' for the attack, which the Iraqis said was a result of mistaken identity. But White House spokesman Marlin Fitzwater said Monday the United States would not be satisfied until it received compensation for the dead crewmen and damaged ship.

President Reagan put U.S. military ships in the Persian Gulf on a heightened state of alert. Fitzwater said Iraqi or Iranian aircraft ''flying in a pattern which indicates hostile intent will be fired upon unless they provide adequate notification of their intentions.''

The attack was the deadliest in the gulf since Iran and Iraq went to war in September 1980 and began attacking commercial shipping in an effort to cripple each other's economies.

The U.S. ambassador to Bahrain, Sam Zakhem, said two Exocet missiles punched holes in the Stark, one on the port side and the second just below the bridge. The Pentagon has said only that one and possibly two missiles hit the ship.

''I heard the alarm and I didn't know where it was coming from at first,'' said crewman James Wheeler, 25, of Texas. ''I heard something whistling and then there was nothing but fire.''

Wheeler and Lawrence Mark Bareford, 23, of Spotsylvania, Va., were moved to a U.S. military hospital in West Germany today for treatment of severe burns. Both spoke to reporters before leaving Bahrain.

Bareford said he heard an explosion.

''Water started coming over the side and I radioed for help,'' he said. ''Then it all went black. ... Please pray for us all over here. I will be home soon, but this wasn't exactly the way I planned on coming home.''

Wounded crew members were rescued from the Stark on Monday, and a 24-member U.S. military medical team was flown to Bahrain to treat them.

The bodies of the dead sailors were transferred to the USS Lasalle, flagship of the U.S. fleet in the gulf. A C141 military transport plane left the Rhine-Main Air Base in West Germany today to pick up the bodies.

In Washington, Iraqi Ambassador Nizar Hamdoon said the Iraqi warplanes may have been aiming for a vessel 20 miles away that was believed to be Iranian. U.S. officials agreed the attack was apparently a case of ''mistaken identity.''

However, officials could not explain why the Stark did not try to shoot down the missiles or the plane. The Pentagon said the ship had at least a minute's warning that a missile was fired.

''We did not return the fire. I don't know the reason,'' said Fitzwater.

The official Soviet press said the attack may have been an accident, but added, ''The constant military presence of the United States there in the Persian Gulf aggravates the danger of the complicated situation.''

The Soviets reported one of their own tankers was damaged in the gulf Saturday night when it struck a mine, but they said there were no fatalities.

The Stark, a 3,585-ton vessel, is part of a seven-vessel U.S. Navy force patrolling the gulf. The Soviet Union, Britain and France also maintain warships in the area to protect ships flying their flags.

Last week, Assistant Secretary of State Richard Murphy met with Kuwaiti officials on plans to register some Kuwaiti tankers in the United States in order to receive protection from U.S. warships.

Prime Minister Hussein Musavi of Iran said the attack demonstrated that the gulf ''is not a safe place for the superpowers.'' He was quoted by Tehran radio, monitored in Cyprus.