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US President Donald Trump has said he is open to sending the New York truck attack suspect to Guantanamo Bay.

"I would certainly consider that," he told reporters at a cabinet meeting. "Send him to Gitmo," the president added, using the prison's nickname.

Mr Trump said "these animals" need to face "far greater" US punishment.

He also pledged to end the green card lottery under which the man suspected of killing eight people in Manhattan on Tuesday entered the US.

The Department of ³ÉÈË¿ìÊÖland Security confirmed the suspect, Uzbek immigrant Sayfullo Saipov, 29, came to the US in 2010 under the diversity visa programme.

The popular 1990 scheme awards US permanent resident visas to around 50,000 applicants from around the world each year.

Speaking at the White House, the president said: "I am today starting the process of terminating the diversity lottery programme.

"I'm going to ask Congress to immediately initiate work to get rid of this programme."

Of the diversity green card, Mr Trump said: "Sounds nice, it's not nice, it's not good - we've been against it."

Can Trump do that?

Analysis by Anthony Zurcher, ³ÉÈË¿ìÊÖ News, Washington

Could Donald Trump send Sayfullo Saipov to Guantanamo Bay? The answer is, it's complicated.

The US government has cited the Authorisation for Use of Military Force (AUMF), passed by Congress in the wake of the 11 September 2001 attacks, as justification for detaining enemy combatants at Guantanamo.

The Supreme Court has held this only applies to those captured who are part of Al Qaeda, the Taliban and "associated forces".

The Obama administration interpreted this language to include individuals affiliated with the so-called Islamic State (IS), but that determination has not yet faced legal challenge.

So Mr Trump could move Saipov to Guantanamo, but the act would confront a number of legal challenges.

Is Saipov - a permanent US resident captured on American soil who may have only been "inspired" by IS - really an enemy combatant?

If so, is action against IS covered by the AUMF? It would be up to US judges to decide.

Two hawkish Republican senators - John McCain and Lindsey Graham - are advocating holding Mr Saipov as an "enemy combatant".

The suspect, who is not a US citizen, allegedly ploughed a rented truck into cyclists and pedestrians on a Manhattan bike path before he was shot by an officer and taken into custody.

Mr Trump told reporters: "We also have to come up with punishment that's far quicker and far greater than the punishment these animals are getting right now.

"They'll go through court for years at the end, who knows what happens."

He added: "Because what we have right now is a joke and it's a laughing stock and no wonder so much of this stuff takes place."

Guantanamo Bay's population of inmates has dwindled from a high of more than 750 to 41.

Former President Barack Obama's administration tried unsuccessfully to close the prison amid claims of abuse and a lack of due process.

Mr Trump has called repeatedly for "extreme vetting" of travellers to the US, and has issued several executive orders blocking citizens from mainly-Muslim countries.

Those executive orders have been blocked by the courts, and are due to be argued before the Supreme Court in the coming weeks.