Pyongyang has conducted a series of missile launches in the wake of its fourth nuclear test in January, despite international condemnation.
Experts have concluded North Korea is able to make nuclear warheads small enough to arm Scud missiles, but it is unclear if they can put weapons on larger rockets which travel further and can deploy warheads from space.
The defence official said: "Truthfully, they have the capability right now to be able to deliver a nuclear weapon, they are just not sure about re-entry, that's why they continue to test their systems out there."He added that he believed North Korea can already "mate" a missile with a warhead.
The Terminal High Altitude Area Defense system will be operational within 10 months, according to the Pentagon, and has sparked strong objections from China and Russia.
Kim Jong-Un inspects the tip of a warhead after a simulated test earlier this year © Reuters Kim Jong-Un inspects the tip of a warhead after a simulated test earlier this year Pyongyang's continued nuclear testing has generated concern in the US military, and the Pentagon has devised contingency plans to try and halt its atomic capabilities.
The official added: "It is the threat that keeps me awake at night.
"You've heard other senior leaders say the same thing, primarily because we don't know what the 'Dear Leader' in North Korea really is after."