His comments, as he arrived in Poland for a Nato summit, came after two more black men died in such incidents.
Philando Castile was shot dead during a traffic stop in Minnesota on Wednesday, while Alton Sterling was shot dead by police in Louisiana a day before.
Mr Obama said the US must say "we're better than this", and that its importance went beyond race.
"This is not just a black issue. It's not just a Hispanic issue. This is an American issue that we should all care about," he said.
"All fair-minded people should be concerned."
