Donald Trump sparked bipartisan backlash after the Republican attacked the bereaved parents of a Muslim US Army captain who spoke at the Democratic convention last week.

Critics from both parties on Saturday questioned whether Trump had the empathy and understanding to be president, particularly after he questioned why mourning mother Ghazala Khan stayed silent during her husband's Thursday night address.

"He was kind of trying to turn that into some kind of ridicule," Democratic vice-presidential nominee Tim Kaine said after a campaign event in Pittsburgh. "It just demonstrates again kind of a temperamental unfitness. If you don't have any more sense of empathy than that, then I'm not sure you can learn it."