In a statement, Mr Obama said no one in the US should be targeted for "what they look like" or "how they worship".
His comments came after criticism from Turkish President Recep Tayyip Erdogan over Mr Obama's silence on the case.
With a suspect in custody, police are still investigating the motive, amid family claims it was a hate crime.
The FBI has opened an inquiry into the case.
Deah
Shaddy Barakat, his wife Yusor Mohammad Abu-Salha and her sister Razan
Mohammad Abu-Salha were found dead on Tuesday evening in their home near
the University of North Carolina, where Mr Barakat was a dental
student.
Craig Hicks, a neighbour of the students, has been
charged with the murders. Mr Hicks' Facebook profile included a photo
that read "Atheists for Equality". He also frequently posted quotes
critical of religion.
A vigil in Chapel Hill drew hundreds
But Mr Hicks' wife Karen said the incident had nothing to do with religion and her husband treated everyone equally.
Mr
Obama called the murders "brutal and outrageous" and said the FBI would
be investigating whether any "federal laws were violated".
"Michelle and I offer our condolences to the victims' loved ones," he said.
"As we saw with the overwhelming presence at the funeral of these young Americans, we are all one American family."
More than 5,000 people attended a funeral on Thursday for the three students.
Neighbours
told the BBC Mr Hicks was involved in a series of parking disputes.
Police also said that their initial investigation showed that there had
been an ongoing parking dispute.
But the BBC's Rajini Vaidyanathan
said many mourners at the funeral feel the murders were sparked by
something far deeper than a parking row.
Mr Obama offered condolences to the victims' loved ones
Family members of the victims say Mr Hicks had previously "picked on" the married couple and deliberately showed his firearm.
Chapel Hill police have said they will investigate every lead, including the possibility of hate crime.
On Thursday, the Turkish president criticised Mr Obama and other top US officials for having not made any statement.
"If
you stay silent when faced with an incident like this, and don't make a
statement, the world will stay silent towards you," he said.
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