A senior US military official has revealed that "almost everything went wrong" during the first military raid carried out under President Donald Trump.

The raid, conducted by the super-secret Joint Special Operations Command in southern Yemen on Sunday, was intended to capture computer equipment from al-Qaeda that could provide valuable intelligence to the US.

Three al-Qaeda leaders were killed, according to US officials. But so, too, were two Americans: Chief Petty Officer William Owens, 36, a member of SEAL Team 6, and eight-year-old Nawar al-Awkaki, the daughter of New Mexico-born former al-Qaeda leader Anwar al-Awlaki - who was killed five years ago in a US air strike.

Owens was killed during a firefight. Three other military personnel were injured during a hard-landing of a V-22 Osprey military aircraft, Pentagon spokesman Jeff Davis confirmed.

The US Defence Department confirmed women who were fighting alongside male troops were also killed during Sunday's battle.

"There were a lot of female combatants," Mr Davis said.

"Female fighters ran to pre-established positions as though they had trained to be ready."

Washington views al-Qaeda in the Arabian Peninsula (AQAP) to be the global terror network's most-dangerous branch.

The raid occurred in the Yakla region of Baida province.

Four others were injured when an Osprey military aircraft (pictured during a training exercise in 2015) crash-landed (Image: EPA)

Fourteen fighters, including women, were killed on the AQAP side. However, the jihadist group claims that number is actually closer to 30 people, including children.

Nawar al-Awlaki's grandfather, Yemen's former agriculture minister, said his granddaughter died two hours after being shot.

"My granddaughter was staying for a while with her mother, so when the attack came, they were sitting in the house, and a bullet struck her in her neck at 2.30 past midnight. Other children in the same house were killed," Mr al-Awlaki told NBC News .

"They [the SEALs] entered another house and killed everybody in it, including all the women. They burned the house. There is an assumption there was a woman [in the house] from Saudi Arabia who was with al Qaeda. All we know is that she was a children's teacher."

A senior US military official also told NBC that "almost everything went wrong."

He added the raid was Mr Trump's first clandestine strike, not a holdover mission approved by President Barack Obama.

However, according to AFP, the raid was in preparation for some time and Mr Obama was aware of it.