Philonise Floyd, a black brother killed by the police, said the phone call between Trump and him was so swift that he could not speak.
"He didn't even give me a chance to say it. It was difficult. I tried to talk, but he was like trying to avoid me like 'I don't want to hear what you're saying'", Philonise Floyd
Calling his brother's death a "modern day murder in modern times," Philonise said he wanted Derek Chauvin, the officer on the foot of George's neck, to be charged with first-degree murder rather than level.
Philonise also added that he expects the other three officers involved in the case to be arrested and charged with first-degree murder and death sentences, although Minnesota is among the 25 states to abolish the sentence.
Philonise said he called the former vice president, Democratic candidate Joe Biden, to ask him to reclaim his justice for George.
"I asked Biden, too. I never had to ask any man, but I asked him if he could please get justice for my younger brother," Philonise Floyd added.
Protests for justice for George Floyd have spread throughout the US cities and increasingly complicated, becoming violent.
Protesters are said to be dissatisfied with the sentence of Chauvin, who was charged with third-degree murder and manslaughter.
US President Donald Trump has condemned the behavior of extremist protesters as "bandits, anarchists".
Floyd's justice demonstrations evoke memories of riots in Ferguson, Missouri, in 2014, after a police officer shot and killed an African-American young man suspected of robbing.