FUJAIRA, United Arab Emirates (AP) _ American passengers said Tuesday that when Iranian marines boarded the cargo ship President Taylor, they feared they were about to become the latest victims in an international cycle of hostage-taking.

''We heard about hostages so often that we were scared of becoming captives when the gun-toting Iranians boarded the ship'' to search it, said Frances Kirner, of Belmont, Calif.

She and her husband Harry, both in their mid-60s, said they were in the cabin just below that of Robert Reimann, captain of the 19,203-ton American freighter, when the Iranians intercepted it Sunday 20 miles off Oman.

The Kirners said six armed Iranian marines boarded and a seventh stayed on the gunboat that pulled alongside the freighter. Iranian naval personnel frequently board commercial vessels in the Persian Gulf area to see if they carry military equipment bound for Iraq. Iran and Iraq have been at war since September 1980.

''The Iranians said good morning to us,'' Mrs. Kirner said. ''They were polite, smiling, but not friendly smiles.''

Capt. Reimann's reaction to such remarks was ''Polite? How polite? To me it was an act of piracy.''

Mrs. Kirner said she overcame her fear, picked up her camera and ''started shooting snapshots'' of the intruders, who did not object.

Harry Kirner, who identified himself as a former U.S. Marine major, said: ''What happened was very stupid, very frightening. The interception was pointless, because the ship was carrying nothing but food to most of the countries that it visited. There were no arms aboard.''

The 610-foot freighter ship was carrying grain from Pakistan to Fujaira when it was intercepted. Its agents said it was to take a shipment of soybeans to India and Indonesia from here.

It dropped anchor late Sunday off this emirate at the eastern end of the Arabian peninsula. The captain and 44 American crewmen spent a day aboard as U.S. Ambassador George Quincey Lumsden Jr. interviewed them and the 12 American passengers checked into a hotel, where they were interviewed by The Associated Press.

The President Taylor, like some other cargo ships, accepts a limited number of bookings from passengers who prefer the longer voyages and less regulated lifestyles aboard freighters to those of luxury cruise liners.

Several passengers said the voyage, which began Sept. 29 at Seattle, Wash., was ''perfectly peaceful'' until the boarding just before the President Taylor entered the Strait of Hormuz.

Crew member Joseph Valverdo of New York said two Iranians spoke fluent English, and one who acted as interpreter said he was educated in South Carolina.

''When it comes to Iranians, you cannot possibly know what they are going to do, so we were scared,'' said Valverdo, 56. ''Now that it is over, I can say it was an exciting experience ... From what we hear, the Iranians are very unpredictable, and they could blow your brains out without batting an eye.''

Capt. Reimann, of Middletown, R.I., said the patrol boat was nine miles away when ''they talked on VHF (radio) and ordered me to stop for inspection. We kept on talking for 10 or 15 minutes. I told them I can't stop, I am a merchant vessel in international waters.

''They threatened that drastic action would be taken unless I stopped, then came closer with their 175-foot-long corvette and 50-caliber twin guns and repeated they would take drastic action unless I stopped,'' he said. ''So I stopped and allowed them to come aboard.''

He said the Iranians came to the bridge and ''tried to apologize, which I did not accept. I considered this an act of piracy.''

They checked the cargo manifest and opened three containers, in which they found cotton, under the chief steward's supervision, the captain said.