The man accused of killing eight people in New York by driving a truck down a cycle lane was inspired by the Islamic State (IS) group, police say.
New York Police's Deputy Commissioner John Miller said that notes in Arabic claiming the attack on behalf of IS were recovered from the scene of the attack in Lower Manhattan.
The suspect, Sayfullo Saipov, a 29-year-old Uzbek immigrant, was shot and injured by police.
He is in hospital and under arrest.
Mr Miller said: "Based on the investigation overnight, it appears that Mr Saipov had been planning this for a number of weeks.
"He did this in the name of Isis [an alternative name for IS], and along with the other items recovered at the scene was some notes that further indicate that.
"He appears to have followed almost exactly to a 'T' the instructions that Isis has put out in its social media channels before, with instructions to their followers on how to carry out such an attack."
One of the notes said "the Islamic State would endure forever", the deputy commissioner added.
Police have sealed off Mr Saipov's home in Paterson, New Jersey, and are searching the premises.
IS has suffered a series of military setbacks in Syria and Iraq in recent months as US-backed forces take back territory the group considers its "caliphate".
What has been the reaction?
New York has increased the police presence at key transport hubs, and there will be additional uniformed and plain-clothes police on duty at Sunday's New York Marathon.
President Donald Trump said he was taking steps to end the diversity lottery programme - the immigration system under which the suspect entered the country.
He also attacked the US justice system, and said he would consider sending the suspect to the US military prison at Guantanamo Bay, Cuba.
"We also have to come up with punishment that's far quicker and far greater than the punishment these animals are getting right now," he said.
The mayor of New York City and the governor of New York state have both praised the resilience of New Yorkers - and urged people not to "politicise" a tragedy that took eight lives.
Governor Andrew Cuomo said the attacker was believed to have acted alone, telling reporters: "He is a depraved coward, is what he is, and he was associated with Isis, and he was radicalised domestically."
Mr Cuomo and Mayor Bill de Blasio also suggested New York's strict gun control laws had ensured that high-powered weapons could not get into the hands of terrorists.
How did the attack unfold?
The attacker rented the truck from a New Jersey branch of retailer Home Depot on Tuesday afternoon before driving to New York City and entering the bike lane, police said.
Video cameras show the van driving at very high speed, appearing to target bike riders and pedestrians.
After the van collided with a school bus, its driver emerged and brandished what appeared to be two weapons.
Mr Saipov was shot and wounded at the scene by police officer Ryan Nash, 28, one of three NYPD officers who attended the scene after being alerted by witnesses.
He is currently being treated at Bellevue hospital, where he has been interviewed by officers.
Knives, a paint gun and a pellet gun were recovered from the scene.
Twelve people were injured in the attack. Three have subsequently been released and nine remain in hospital, five of them in a serious condition.
It was the deadliest terror attack in the city since 11 September, 2001, when nearly 3,000 people died at the hands of al-Qaeda attackers who flew hijacked aircraft into the twin towers of the World Trade Center.
Who is the suspect?
Sayfullo Saipov had reportedly lived in Tampa, Florida, before moving to Paterson, New Jersey.
He arrived in America from Uzbekistan in 2010 and is a legal resident in the country. Uber confirmed he had been working as a driver for them.
CBS News quotes an intelligence source as saying he was known to US authorities after his name was associated with the subjects of FBI counter-terrorism investigations in 2015.
The source says he had some contact with individuals who were considered radicalised extremists, at least one of whom was Uzbek. It is unclear whether those being investigated were in the US or overseas.
It is unclear if Mr Saipov, who was not the main focus of the investigation, was interviewed at that time by the FBI.
Uzbekistan's President Shavkat Mirziyoyev told President Trump his country was ready to "use all forces and resources" to help investigate the attack. Uzbek officials have not yet confirmed the identity or nationality of the attacker.
Who were the victims?
The deaths of five Argentines were confirmed by the country's foreign ministry. They were part of a group of nine friends in New York to celebrate the 30th anniversary of their graduation from a polytechnic college in the central city of Rosario, Argentine media said.
One of the men who died, steel firm owner Ariel Erlij, helped pay for the friends' trip, La Nación newspaper reported (in Spanish).
The men - all aged 48 or 49 - were named as Hernán Diego Mendoza, Diego Enrique Angelini, Alejandro Damián Pagnucco, Ariel Erlij and Hernán Ferrucci.
Belgian officials said Anne-Laure Decadt, a 31-year-old from Staden in Flanders, was also killed. Three Belgians were wounded.
Two other victims, both Americans, have not yet been named.
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