Former US Secretary of State and Democratic presidential nominee Hillary Clinton has asked President Donald Trump to "step up and speak out" on rising hate crimes in the US, in the wake of the killing of Indian engineer Srinivas Kuchibhotla in a Kansas City bar last week.

"With threats & hate crimes on rise, we shouldn't have to tell @POTUS to do his part. He must step up & speak out," Clinton tweeted.

The Democratic presidential nominee, who was thought to be a favourite to win the November elections, lost to Donald Trump of the Republican Party.

Her comments came as the body of Kuchibhotla was flown to India and cremated on Tuesday in Hyderabad with grieving relatives, friends and neighbours gathering for the last rites.

Kuchibhotla, 32, was shot dead by a US Navy veteran, Adam Purinton, 51, in an apparent hate crime.

Purinton shot dead Kuchibhotla while his friend Alok Madasani was injured at a pub in Kansas.

Purinton, 51, made his first court appearance in the case that is being investigated as a possible hate crime.

Purinton appeared before a Johnson County District Court judge via video conference on Monday. He faces one charge of first-degree murder and two charges of attempted first-degree murder in last Wednesday's shooting at the bar in Olathe, Kansas.

On Friday, the widow of Kuchibhotla sought answers to what she perceived was a spread in American hate crimes.

"I have a question in my mind: Do we belong?" said Sunayana Dumala, who like her husband travelled from India to attend a US college.

"We've read many times in newspapers of some kind of shooting happening," she said at a news conference at the headquarters of Garmin, where Kuchibhotla worked as an aviation systems engineer. "And we always wondered, how safe?"

While President Trump is yet to comment on the shooting, White House press secretary Sean Spicer said last week that it was too early to call the act a hate crime. 

Spicer also referred to the shooting at a news conference on Monday while addressing President Trump's concerns against recent acts of vandalism against Jewish cemeteries in St Louis and Philadelphia.

"No one in America should feel afraid to follow the religion of their choosing freely and openly. The president has dedicated to preserving this originating principle of our nation," Spicer said.

"And while we're at it, I don't want to get ahead of law enforcement, but I was asked the other day about the story in Kansas, the shooting in Kansas. And while the story is evolving, early reports out of Kansas are equally disturbing," he said.