Donald Trump is being urged to publicly condemn a white US army veteran who is accused of killing a black man with a two-foot sword in a racially-motivated attack.

Prosecutors say James Harris Jackson launched a vicious attack on Timothy Caughman in New York on Monday, however the US President is yet to address the killing.

Jackson told police he had been harbouring feelings of hatred towards black men for at least 10 years after he was arrested on suspicion of murder.

He turned himself in at a Times Square police station about 25 hours after he allegedly killed Mr Caughman, who had staggered into a precinct bleeding to death.

"The defendant was motivated purely by hatred," said Assistant District Attorney Joan Illuzzi, who added that the charges could be upgraded, "as this was an act most likely of terrorism."

Mr Trump’s radio silence on the attack has been greeted with public outcry, with many Americans urging him to label Jackson a “white supremacist” and recognise the killing as a “terror attack”.

On Thursday he tweeted his condolences to US tourist Kurt Cochran who was killed in the London terror attacks.

“A man named Timothy Caughman was killed on Monday in NYC by a white supremacist in a terrorist attack. Maybe send condolences to his family,” one man wrote in a tweet directed to Mr Trump.

“Imagine the headlines if a Muslim would have travelled to New York and murdered a white man with a sword. A sword…,” another wrote.

Many others have highlighted the the issues Mr Trump felt compelled to tweet about since being elected president.

“Can you imagine what the outcry would be if @SnoopDogg, failing career and all, had aimed and fired the gun at President Obama? Jail time!” Mr Trump wrote in a recent tweet.

“My daughter Ivanka has been treated so unfairly by @Nordstrom. She is a great person -- always pushing me to do the right thing! Terrible!” he wrote in another.

Authorities said Jackson came to New York last week to make a splash in the media capital of the world by killing as many black men as possible.

He was armed with two knives and told officers he had tossed the sword in a bin in Washington Square Park, officials said. It was later recovered.

Investigators said they were trying to determine exactly what drove Jackson to violence. They planned to search his laptop and phone and interviewed friends and family.