At least eight people died Tuesday in lower Manhattan after a truck driver careened his vehicle into pedestrians and then yelled “Allahu akbar” in an attack that is being investigated as Islamist terrorism.

Authorities did not publicly name the attacker, but he was identified as Sayfullo Saipov, a 29-year-old immigrant from Uzbekistan who pledged allegiance to the Islamic State — details that prompted President Trump to order stiffer controls on immigration.

“This was an act of terror, a particularly cowardly act of terror, aimed at innocent civilians, aimed at people going about their lives who had no idea what was about to hit them,” New York Mayor Bill de Blasio said at an evening news conference. Besides the eight deaths, at least 11 people were badly injured, he said.

The attacker drove a white Home Depot rental truck in the wrong direction down a bicycle path near Stuyvesant High School along Manhattan’s West Street and Chambers Street.

After driving 14 blocks and crashing into a school bus just after 3 p.m., he exited the car displaying two firearms — a paintball gun and a pellet gun. He was shot in the abdomen by police officers and taken into custody, said James P. O’Neill, commissioner of the New York Police Department.

He was hospitalized and had surgery Tuesday evening and is expected to live.

Eyewitnesses reportedly told authorities that the driver exited the cab yelling “Allahu akbar,” the Arabic phrase for “God is great” and a jihadi war cry. When asked about those news reports, Mr. O’Neill acknowledged without elaborating that the attacker had said something that suggested terrorism.

Law enforcement officials told reporters that a note was recovered inside the truck, possibly written in Arabic, that also suggested the act was Islamic State-inspired terrorism. The FBI’s Joint Terrorism Task Force has joined the investigation.

Rep. Michael T. McCaul, Texas Republican and chairman of House Homeland Security Committee, told Fox News that the attack was “‘the ninth vehicle assault” inspired by the Islamic State.

Islamist sympathizers in Nice, France; Barcelona, Spain; London; and Berlin have all used trucks as weapons in mass-fatality attacks. The Islamic State has urged its sympathizers to use such tactics in “crusader” nations for a couple of years.

New York Gov. Andrew Cuomo said at the press conference that the attacker seemed to be a “lone wolf” who was not involved in “a wider plot, a wider scheme.”

But Dan Bongino, a former Secret Service agent, called that very mode of attack frightening because, unlike when al Qaeda would spend millions of dollars training a handful of airplane pilots, driving a truck is cheap, requires little effort and “leaves few investigative footprints.”

“What are we going to have — a ‘do not rent’ list?” he asked rhetorically on Fox News.

Numerous news organizations, starting with ABC News, reported that the suspect had been identified as Sayfullo Habibullaevic Saipov from Tampa, Florida. He had a Florida driver’s license, but other authorities said he may have resided in New Jersey.

The photo CBS News released of Saipov, who the network said was from Uzbekistan, showed him in a full Muslim beard.

Fox News reported that Saipov arrived in the U.S. as a legal immigrant in 2010, courtesy of the diversity visa program, essentially a worldwide lottery system. Mr. Trump has proposed eliminating the program.

Late Tuesday night, Mr. Trump took to Twitter to announce a crackdown, though he didn’t elaborate on details. His earlier efforts to tighten limits on immigrants and refugees, especially from majority-Muslim nations, have been blocked by U.S. courts.

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

Earlier in the day, Mr. Trump implied that the attack was a result of U.S. immigration authorities allowing Islamic State terrorists to enter the country.

“We must not allow ISIS to return, or enter, our country after defeating them in the Middle East and elsewhere. Enough!” Mr. Trump had tweeted.

There was no immediate claim of responsibility from the Islamic State, al Qaeda or any other terrorist group.

However, pro-Islamic State websites were openly exulting in the attack, and terrorism analyst Rukmini Callimachi reported that a French ally of the Islamic State had issued an unusually specific threat against Halloween gatherings in the West on Monday.

Though there have been failed attempts, Tuesday’s attack was the first terrorist act to claim casualties in New York since Sept. 11, 2001. It took place just blocks away from the National Sept. 11 Memorial.

Mr. de Blasio and Mr. Cuomo reminded New Yorkers that they had weathered terrorist attacks before and rose to the challenge.

“We know this action was intended to break our spirit. We have been tested before,” the mayor said. “New Yorkers do not give in in the face of these kinds of actions.”

They also defiantly said that the planned Halloween evening parade in nearby Greenwich Village would go ahead as scheduled. Mr. de Blasio was at the parade, inspecting security and living out his advice for New Yorkers to be vigilant but go ahead with their plans.

Mr. Cuomo ordered tighter security at New York’s airports, tunnels, bridges and transit systems and stepped up patrols at large public gatherings.

He also announced that the spire at 1 World Trade Center be lit up in red, white and blue.

There was no immediate identification of the victims, but five of the dead were from Argentina and one from Belgium, those nations’ foreign ministers said.

Witness Greg Ahl told a local CBS affiliate that “a vehicle drove straight down a bicycle path heading south in Manhattan just mowing everything down. It looks like a vehicle drove down the bicycle path and ran everything over.”

Another eyewitness, Eugene Duffy, told CNN that when he came across the scene he saw people lying on the ground with tire tracks across their bodies. He said the truck had crashed into another vehicle and come to a stop. That was when he heard gunfire, presumably from the police.

“Once all the screaming stopped, you heard all the gunshots. Nine or 10 gunshots,” he said.

Authorities said the truck was apparently rented at a Home Depot in Passaic, New Jersey, about an hour before the attack. Late in the evening, they had cordoned off and surrounded a white Toyota minivan with Florida plates in the Home Depot lot, checking it out for clues and booby traps.

Home Depot spokesman Matthew Harrigan told reporters that the company is “fully cooperating” with law enforcement.

⦁ S.A. Miller and Andrea Noble contributed to this article, which is based in part on wire service reports.

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