WINSTON-SALEM, North Carolina (REUTERS) - US President Barack Obama described the deaths of three young Muslims gunned down in North Carolina as "brutal and outrageous murders" on Friday and said no one in the United States should be targeted for their religion.

The President's statement came a day after the FBI said it would open a preliminary inquiry, separate from local police investigations, to determine whether the man accused in the Chapel Hill shooting on Tuesday broke any federal laws.

"No one in the United States of America should ever be targeted because of who they are, what they look like, or how they worship," Obama said in a statement, offering his condolences to the victims' families.

The families had called on Obama to insist that federal authorities investigate whether the murder suspect, 46-year-old paralegal student Craig Stephen Hicks, was motivated by hatred toward the victims because they were Muslim.

Newlywed Deah Shaddy Barakat, 23, a University of North Carolina dental student, his wife Yusor Mohammad Abu-Salha, 21, and her sister, Razan Mohammad Abu-Salha, 19, a student at North Carolina State University, were killed in a condominium about 3km from the UNC campus.

On Thursday, Turkish President Tayyip Erdogan criticised Obama and other US leaders for their silence about incident, which has garnered international attention and left some US Muslims feeling concerned about their safety.

United Nations Secretary-General Ban Ki-moon on Friday praised the three victims, who were all involved in humanitarian aid work, as representing the best values of global citizenship and said he was deeply moved by scenes of thousands of people mourning their deaths.

The FBI has not specified if its inquiry would include whether the shooting was a hate crime.

Local police cited a parking dispute as Hicks' motive but said they were also looking into whether religious hatred played a role.

Neighbours said Hicks, who posted anti-religion messages and a photo of a gun he said belonged to him on his Facebook page, was known in the condo community as someone prone to grow angry over parking troubles and noise.

Mohammad Abu-Salha, the father of the two female victims, told CNN that his daughter Yusor had said Hicks made her feel uncomfortable after she moved into a neighbouring condo where her new husband lived.

"Daddy, I think he hates us for who we are," Abu-Salha said his daughter told him, according to CNN.