US President Donald Trump says that the Daesh (ISIL) terrorist group will pay a "big price" for every attack it carries out in the United States, following the New York truck attack by an alleged ISIL loyalist.

Axar.az reports citing Press TV that Trump said on Friday that the US military has hit ISIL "much harder" over the past two days after the group claimed the attacker was one of their "soldiers."

"They will pay a big price for every attack on us!" Trump wrote on Twitter.

In the wake of the attack, Trump said he had ordered the Department of Homeland Security to step up “our already extreme vetting” for immigrants entering the United States.

On Tuesday, a 29-year-old Uzbek man rammed a truck into cyclists and pedestrians in New York City, killing at least eight people and injuring 12 others. Authorities swiftly branded the attack an "act of terrorism."

The suspect was identified as Sayfullo Saipov. He is from Uzbekistan in Central Asia but has been living in the US since 2010.

Law enforcement authorities said Saipov had been inspired by ISIL's violent ideology.

On Wednesday, Trump suggested in a tweet that the suspect should be executed.

Trump initially said he might send Saipov, who he called an “animal,” to the US military prison at Guantanamo.

The latest incident came five months after a speeding vehicle hit pedestrians on a sidewalk in New York City’s Times Square on May 18, killing at least one person and injuring 22 others.

The US claims to be fighting ISIL in several countries but critics say the American government and its allies have encouraged the spread of Daesh in the Middle East to create a perpetual war in the region and advance the US military-industrial complex.