DUBAI (Reuters) - One crew member was wounded when Yemen's Houthis fired a missile at a United Arab Emirates ship carrying medical supplies in the Red Sea, the UAE news agency WAM reported on Thursday.

WAM quoted a statement from the UAE armed forces as saying that the ship came under attack opposite the Yemeni port of al-Mokha. The statement warned that the UAE would pursue those behind the attack.

"The attack did not cause any damage to the ship, while a crew member was hurt," WAM said.

The Saudi state news agency earlier quoted the Saudi-led military coalition, which includes the UAE, as saying the ship was hit while leaving al-Mokha port but gave no further details.

WAM gave no details about the medical supplies aboard the ship but noted that the UAE had been sending medicines and medical equipment to help fight a cholera epidemic that had killed nearly 1,000 people in Yemen since April.

The Houthis had reported the attack earlier, broadcasting a grainy video of what Houthi-run media said was a missile being fired at a Saudi-led coalition vessel. The missile burst into a ball of fire as it hit its target.

The attack was part of a protracted conflict between the Iran-aligned Houthis and the Saudi-led coalition. The coalition wants to restore the government of President Abd-Rabbu Mansour Hadi, whom the Houthis have forced into exile.

Al-Mokha was captured by the coalition from the Houthis earlier this year after heavy fighting. It lies close to the Bab al-Mandab shipping lane through which much of the world's oil passes.

Several such attacks were reported since last year against Saudi, Emirati and U.S. ships in the Red Sea.

In January, two crew members of a Saudi frigate were killed in an attack close to Hodeidah port. The U.S. Navy said an unmanned remote-controlled boat laden with explosives hit the ship. The Houthis said they had fired a missile.

Last October, the Houthis fired a missile at an Emirati ship in the strategic Bab al-Mandab strait in what it described as an "act of terrorism."

(Reporting by Mostafa Hashem; Writing by Rania El Gamal; Editing by Leslie Adler, Larry King and Toby Davis)