Americans were united in grief, outrage and "resolve to defend our people", he said.
Omar Mateen, 29, killed 50 people and wounded 53 at the Pulse club before being shot dead by police.
The so-called Islamic State group has said it was behind the attack, but the extent of its involvement is not clear.
A statement on its affiliated Amaq news agency said that an IS "fighter" was responsible.
NBC News reported that Mateen had called the emergency services before the attack and swore allegiance to IS.