"Would love to send the NYC terrorist to Guantanamo but statistically that process takes much longer than going through the Federal system," Trump wrote in a blast of early morning tweets.
Trump added: "There is also something appropriate about keeping him in the home of the horrible crime he committed. Should move fast. DEATH PENALTY!"
Tuesday's attack with a rented truck on a bike path in New York City left eight dead and 12 wounded.
Trump first raised the idea of sending him to Guantanamo yesterday, saying he would consider it, and late that night wrote on Twitter that the attacker "SHOULD GET DEATH PENALTY!"
Since the first inmates arrived at Guantanamo in 2002, only eight have been convicted in the problem-plagued military commissions that have been established there, according to Human Rights Watch. But three of those convictions were overturned and another three have been partially invalidated.