President Joe Biden said the strike on Tower 22 near the Syrian border had been carried out by an Iranian-backed militia, and marked a significant escalation in the growing conflict in the Middle East.
Mr Biden said US forces would hold those responsible to account “at a time and in a manner of our choosing”, as facts about the attack were still being gathered.
“Today, America’s heart is heavy,” the president said in a statement.
“We know it was carried out by radical Iran-backed militant groups operating in Syria and Iraq.
“These service members embodied the very best of our nation: unwavering in their bravery. Unflinching in their duty.
“Unbending in their commitment to our country – risking their own safety for the safety of their fellow Americans, and our allies and partners with whom we stand in the fight against terrorism.”
US Central Command initially said 25 troops were also injured in the strike, which took place early on Sunday morning.
A US official later told Reuters that at least 34 service members were being evaluated for possible traumatic brain injury.
Several of the wounded were transported to separate military facilities for care.
The identities of the deceased are being withheld for 24 hours until their next of kin can be notified.
Tower 22 is situated in northeastern Jordan across the border from the Al-Tanf garrison in Syria, where US forces have teamed up with local forces to confront Islamic State.
An Iranian militia group known as the Islamic Resistance in Iraq has claimed responsibility for three simultaneous drone attacks on US forces, including the deadly Tower 22 assault.
A statement released by the Islamic Resistance threatened more attacks “if the US keeps supporting Israel”. “All the US interests in the region are legitimate targets and we don’t care about US threats to respond, we know the direction we are taking and martyrdom is our prize,” it said.
David Cameron, the UK foreign secretary, said Britain “strongly condemns attacks by Iran-aligned militia groups against US forces”.
“We continue to urge Iran to de-escalate in the region. Our thoughts are with those US personnel who have lost their lives and all those who have sustained injuries, as well as their families,” Lord Cameron added.
Jordanian officials say the attack occurred on Syrian territory at the Al-Tanf base.
Speaking to public broadcaster Al-Mamlaka television, Jordanian government spokesperson Muhannad Al Mubaidin denied that the dead and injured US troops had been stationed in their country, Reuters reported.
The deadly drone strikes came amid increasing fears that the Israel-Hamas conflict could grow into a wider regional conflict.
“Last night, three US service members were killed, and many wounded, during an unmanned aerial drone attack on our forces stationed in northeast Jordan near the Syria border,” President Biden wrote on X, formerly Twitter, on Sunday.
“Jill and I join the families and friends of our fallen in grieving the loss of these warriors in this despicable and wholly unjust attack.”
In a statement released on Monday, Iran’s mission to the United Nations distanced itself from the attack. “Iran had no connection and had nothing to do with the attack on the US base.”
Published by the state news agency IRNA, it added: “There is a conflict between US forces and resistance groups in the region, which reciprocate retaliatory attacks.”
Republican senator Tom Cotton, of Arkansas, called on the US to respond with “devastating military retaliation against Iran’s terrorist forces”, adding: “Anything less will confirm Joe Biden as a coward unworthy of being commander-in-chief.”
He blamed Mr Biden for emboldening Iran by “tolerating attacks on our troops, [and] bribing the ayatollahs with billions of dollars”. Senator Cotton: “He left our troops as sitting ducks and now three are dead and dozens wounded.”
Mark Hertling, a former commander of the US army in Europe, said the Iranian-backed paramilitary forces had presented a “continuous challenge” over the past decade.
“Many think it’s easy to ‘eliminate’ this threat. It isn’t,” Mr Hertling wrote in a post on X.
Tensions have been inflamed by Israel’s invasion of the Gaza Strip, where more than 25,000 Palestinians have been killed and a United Nations aid agency has warned faces an imminent famine.
Nine countries have suspended funding to the United Nations Relief and Works Agency (UNRWA) over allegations its workers took part in the 7 October attacks in Israel, which claimed around 1,200 lives. A further 250 people were taken hostage.
Since Israel’s war on Hamas began, US troops stationed in Iraq and Syria have faced regular drone and missile attacks on their bases.
Some 70 US and coalition soldiers have been injured in attacks in Iraq and Syria since October, most of which were classified as minor, a military official said during a press briefing last week.
The attack in Jordan marks the first time Americans have been targeted in Jordan during the war.
Jordan is a close US ally in the region, and around 3,000 American troops are stationed there.
Mr Biden, who was in Columbia, South Carolina on Sunday, was briefed by defence secretary Lloyd Austin, national security adviser Jake Sullivan and principal deputy national security adviser Jon Finer.