Speaking in China, Mr Obama said the player had raised legitimate issues.
Mr Kaepernick stirred controversy when he sat during the national anthem to protest against racial injustice.
Some players have followed his example and sat or kneeled through the anthem.
Asked about the issue during a news conference at the G20 in Hangzhou, President Obama said it was tough for those in the military to understand why Mr Kaepernick might snub the national anthem.
But he said he did not doubt his sincerity to raise issues.