ABU DHABI—A U.S. Navy ship fired on a small boat in the Persian Gulf, killing at least one crew member, in a reflection of rising tensions in the region.

The USNS Rappahannock, a refueling ship with a mostly civilian crew, fired a .50-caliber machine gun on the small boat in the waters off the United Arab Emirates on Monday.

The smaller vessel was a fishing boat, an Emirati diplomat said in a statement. One Indian fisherman was killed and three Indian nationals were critically injured, said U.A.E. deputy foreign affairs minister Tareq Al Haidan.

A spokesman at India's Ministry of External Affairs couldn't be reached for immediate comment.

The shooting occurred close to the entrance of the port of Jebel Ali, the diplomat said, adding that Emirati authorities are investigating the matter.

U.S. officials defended the actions of the Rappahannock, saying the small vessel ignored a series of nonlethal warnings. "The safety of our vessels and our personnel is our utmost priority. Our ships have an inherent right of self-defense against potential threats," said Lt. Greg Raelson, a spokesman for the Navy's Fifth Fleet. "In this situation you had a small motor vessel that was deliberately approaching and did not respond to any warnings."

Navy supply ship Rappahannock in the South China Sea in March. US Navy/Reuters

Small boats laden with explosives pose significant risks to U.S. Navy ships, and could potentially disable a ship and wound or kill crew members. Iranian fast boats frequently buzz warships patrolling the Persian Gulf, prompting Naval officers to fire warning shots.

A series of near-miss incidents in the Persian Gulf, including boats from Iran's Revolutionary Guard threatening Western warships, has prompted the U.S. military to propose a hotline with Tehran to prevent accidental escalations.

U.S. officials said the small boat wasn't Iranian. There were six people aboard, officials said.

Small fishing boats that dot the waters of the Persian Gulf are frequently owned by Emiratis or Iranians but are generally operated by crew members of other nationalities.

The Rappahannock's response seemed appropriate, said Michael Corgan, professor at Boston University, citing the 2000 attack on the USS Cole by a small boat laden with explosives.

"No US Navy skipper wants to be another USS Cole," he said. "Any speedboat closing a man-of-war or military ship in those waters at high speed is asking for it."

U.S. officials wouldn't describe the warning protocols, which typically include warning shots and verbal commands in multiple languages to change direction.

"The crew repeatedly attempted to warn the vessel, and everything was done in accordance with Navy force-protection procedures," said Lt. Raelson. "The vessel disregarded the warnings and that is when lethal force was resorted to."

The incident occurred about 2:30 p.m. local time in the territorial waters of the U.A.E., about 10 miles from Jebel Ali, the Emirates' main container port and a point where U.S. naval vessels frequently stop to refuel. The Rappahannock was traveling to the UAE to make a port call.

Write to Julian E. Barnes at julian.barnes@wsj.com and Margaret Coker at margaret.coker@wsj.com