“At this time we have not found any evidence to link this to a hate crime,” Conroe Police Department Sgt David Dickenson told CNN.
Miles Joseph Fridrich, 24, was arrested near the crime scene on a first-degree murder charge over the killing of Khan.
Authorities say that a motive for the killing of the mother of two has not yet been established and an investigation is ongoing.
Muslim advocacy group the Council on American-Islamic Relations says that it is monitoring the situation.
“We are unsure at this moment if this was a hate crime; however, given the tragic circumstances, we are paying very close attention to the investigation,” CAIR’s Houston office said in a statement.
“While the police have not released a motive for the killing, we want to assure everyone that we are in conversation with law enforcement agencies.
“We will continue to monitor the situation while we launch our own investigation and continue to establish dialogue with law enforcement.”
The Anti-Defamation League has also called on police to investigate the killing as a hate crime.
“While the investigation is underway, we strongly call for law enforcement to examine the potential that this murder was motivated by hate,” the ADL said in a statement.
“Hate against one of us, is hate against all of us, and we should not tolerate it ever, anywhere.”
The suspect is being held on a $500,000 bond after making his first court appearance.
“I lost my baby sister. It’s very emotional for us. It was such a senseless murder. We are still trying to wrap our heads around it,” Khan’s brother, Wajahat Nyaz, told KTRK.
“To get justice for this is very important. A murder like this should not go unpunished. It’s bad for the entire community and entire country.”