Trump’s comment amplified his vow to inflict “serious retaliation” after two US Army soldiers and a US interpreter were killed in the attack Saturday in the Syrian city of Palmyra during counterterrorism operations.

The gunman was killed, according to US Central Command. Syria’s state-run Sana news agency reported Sunday that security forces arrested five suspects in relation to the attack. Trump said two of three Americans wounded in the ambush are out of the hospital and the third “is going to be OK.”

“I can tell you in Syria, there will be a lot of damage done to the people that did it,” Trump said during a holiday reception at the White House. “They got the person – the individual person – but there will be big damage done.”

Trump emphasised the Islamic State link while praising Syria’s government, which the US has embraced as an ally after the fall of former President Bashar Al-Assad last December.

“It was ISIS,” Trump said. “The Syrian government fought by our side. The new president fought by our side.”

Trump paid respects to the US casualties in Syria as well as the victims of shootings at Brown University in Rhode Island and at Bondi Beach in Sydney.

Syrian foreign minister Asaad Al-Shaibani and US secretary of state Marco Rubio spoke by phone Sunday to discuss the “terrorist ambush” on US personnel in Syria, according to a separate state department readout.

Al-Shaibani stressed importance of working side by side with “international partners,” including the US, to boost joint efforts to fight terrorism. Rubio pledged continued support for Syria, including its economic recovery and fighting terrorism, Sana reported in its account of the call.

The US readout said Al-Shaibani reiterated the Syrian government’s commitment “to degrade and destroy the shared threat of ISIS.”