Donald Trump has responded to a terrorist attack in New York by vowing to toughen restrictions on immigration.

“I have just ordered Homeland Security to step up our already Extreme Vetting Program. Being politically correct is fine, but not for this!” the President wrote on Twitter.

Throughout his rise to the presidency, Mr Trump has invoked the threat of terrorist attacks as a rationale for tightening immigration policies, including halting refugee admissions and banning immigrants from certain Muslim-majority countries.

Mr Trump's tweets suggest that the President will double down on that push in response to Tuesday's attacks. Earlier in the day, he wrote that “We must not allow Isis to return, or enter, our country after defeating them in the Middle East and elsewhere”.

As a coalition of Iraqi troops, Kurdish forces and others have pushed Isis fighters from vast swathes of territory they seized across the Middle East, terrorism experts have cautioned that loyalists will turn to inflicting violence on Western cities.

Officials deemed the assault in New York, which left eight dead, an act of terrorism.

Multiple news outlets have reported that authorities found a note pledging fealty to Isis in or near the truck assailant Sayfullo Saipov used to mow down bystanders. New York Police Commissioner James O’Neil told reporters witnesses heard the man shout “Allahu Akbar”.

New York Truck attack Show all 6 1 /6 New York Truck attack New York Truck attack Investigators inspect the truck following the attack Investigators inspect a truck following a shooting incident in New York on 31 October 2017. Several people were killed and numerous others injured in New York on Tuesday when a suspect plowed a vehicle into a bike and pedestrian path in Lower Manhattan, and struck another vehicle on Halloween, police said. A suspect exited the vehicle holding up fake guns, before being shot by police and taken into custody, officers said. The motive was not immediately apparent. Getty New York Truck attack A paramedic looks at a body along the bike path A paramedic looks at a body covered under a white sheet along the bike path 31 October 2017, in New York. A motorist drove onto a busy bicycle path near the World Trade Center memorial and struck several people Tuesday, police and witnesses said. AP Photo/Bebeto Matthews New York Truck attack The truck driver collided with a school bus Authorities respond near a damaged school bus Tuesday, 31 October 2017, in New York. A motorist drove onto a busy bicycle path near the World Trade Center memorial and struck several people, police and witnesses said. Two adults and two children were on the bus at the time. AP Photo/Bebeto Matthews New York Truck attack A young girl reacts to the scene A young girl reacts as police officers secure an area following a shooting incident in New York on 31 October 2017. Several people were killed and numerous others injured in New York on Tuesday after a vehicle plowed into a pedestrian and bike path in Lower Manhattan, police said. 'The vehicle struck multiple people on the path,' police tweeted. 'The vehicle continued south striking another vehicle. The suspect exited the vehicle displaying imitation firearms & was shot by NYPD.' DON EMMERT/AFP/Getty Images New York Truck attack Police officers arrive at the scene Police officers arrive at the scene following a shooting incident in New York on 31 October 2017. Multiple people were hurt in downtown Manhattan, US media reported after police confirmed that they were responding to reports of a shooting. Police said they had mobilized to the scene in Lower Manhattan and that one person was in custody, giving no further details. DON EMMERT/AFP/Getty Images New York Truck attack Emergency personnel respond to truck attack in lower Manhattan Emergency personal respond after reports of multiple people hit by a truck after it plowed through a bike path in lower Manhattan on 31 October 2017 in New York City. According to reports up to six people may have been killed. Kena Betancur/Getty Images

Reports said Saipov, a native of Uzbekistan, had come to America in 2010.