DUBAI - Dubai's police chief has rejected US claims that a navy ship warned Indian fishermen to move away from it before firing and killing one of them after they failed to heed the order, media reported on Thursday.

The fisherman died and three others were wounded on Monday when the ship opened fire on their vessel near the port of Jebel Ali off Dubai in the tense waters of the southern Gulf.

The "Indian fishermen were not warned to move away by the US Navy," General Dahi Khalfan said, according to Khaleej Times daily.

"The crew ... told the Dubai police that they did not move towards the ship and instead attempted to avoid it."

"According to our findings and testimonies of the injured, I believe that they told the truth," the daily quoted Khalfan as saying.

On Tuesday, India urged the UAE to investigate the shooting.

Khalfan criticised the way the US ship had dealt with the incident, saying it had moved into international waters right after the shooting. Dubai police will deal with the case as a "murder," he said.

US defence officials said the fishing boat had ignored warnings not to approach the refuelling ship USNS Rappahannock, and that sailors on board the American vessel feared it could pose a threat.

"Since 2000 we've been very concerned about small boats," a defence official said, referring to the year of a deadly suicide bomb attack by Al-Qaeda against the destroyer USS Cole in the Yemeni port of Aden that killed 17 US sailors.

The US Navy has been building up its forces in the oil-rich Gulf region amid mounting tensions with Iran over its controversial nuclear programme.

Tehran has warned it could close the Strait of Hormuz in the southern Gulf if international sanctions begin to bite, potentially disrupting shipping and world oil supplies through the strategic waterway.

Washington has deployed two aircraft carriers to the region -- the USS Abraham Lincoln and the USS Enterprise -- and doubled its mine-sweeper fleet in the area from four to eight ships.

On Monday, the Pentagon confirmed that it had brought forward the deployment of a third strike group, led by the carrier USS John C Stennis, by four months, in order to further bolster its presence.