Three other injured US troops were “doing well”, Trump said.
The soldiers “were conducting a key leader engagement” in support of counter-terrorism operations when the attack occurred, Parnell said, while US envoy to Syria Tom Barrack said the ambush targeted “a joint US–Syrian government patrol”.
The deceased troops’ identities would be withheld until after their families were notified, Centcom said.
The incident is the first of its kind reported since Islamist-led forces overthrew longtime Syrian ruler Bashar al-Assad in December last year, and rekindled the country’s ties with the United States.
Trump said Syria’s new President Ahmed al-Sharaa, who visited the White House last month, was “extremely angry and disturbed by this attack”.
‘Infiltration’
A Syrian military official who requested anonymity said that the shots were fired “during a meeting between Syrian and American officers” at a Syrian base in Palmyra.
A witness, who asked to remain anonymous, said he heard the shots coming from inside the base.
However, a Pentagon official speaking on the condition of anonymity told AFP that the attack “took place in an area where the Syrian President does not have control”.
In an interview on state television, Syrian Interior Ministry spokesman Anwar al-Baba said there had been “prior warnings from the internal security command to allied forces in the desert region” of a potential Isis “infiltration”.
“The international coalition forces did not take the Syrian warnings of a possible Isis infiltration into consideration,” he said.
According to the Syrian Observatory for Human Rights monitor, which has a wide network of sources inside Syria, the meeting came as part of an “American strategy to strengthen its presence and foothold in the Syrian desert”.
Sana reported that helicopters had evacuated the wounded to the Al-Tanf base in southern Syria, where American troops are deployed as part of the Washington-led global coalition against Isis.
Last month, during Syrian President Ahmed al-Sharaa’s historic visit to Washington, Damascus formally joined the coalition.
Isis seized swathes of Syrian and Iraqi territory in 2014 during Syria’s civil war, before being territorially defeated in the country five years later.
Its fighters, however, still maintain a presence, particularly in Syria’s vast desert.
US forces are deployed in Syria’s Kurdish-controlled northeast as well as at Al-Tanf near the border with Jordan.
– Agence France-Presse