Trump gave an interview that was carried on a Kremlin-backed Russian news outlet
The pair talked about Iraq, third-party candidates, and immigration.
King asked the real-estate magnate about his plan for Iraq, but Trump refused to give specifics.
"Honestly, I don't like talking about it," Trump said. "I don't want to have to tell the enemy - in order to get two extra votes - exactly what my plan is, when we're going in, what we're going to do. No, I have a very distinct plan, always subject to change of course."
Trump blamed President Barack Obama for the rise of ISIS because of the way he got the troops out of Iraq.
"The timetable was arranged by Bush for the leaving," King interjected.
"Well, you know what, Larry," Trump said, "I'll tell you what, let's look to the future."
King asked Trump whether he thought the fact that Libertarian candidate Gary Johnson appeared to have little knowledge of Aleppo - the city in Syria ravaged by the country's bloody civil war - would hurt his chances of becoming president.
Trump said he didn't think it would, and that if it did, he probably wouldn't gain many of Johnson's supporters.
King then asked if he'd like Johnson or Green Party candidate Jill Stein to be invited to the presidential debates.
"I'd rather it be Hillary and myself because we're the only two with a chance of winning," Trump replied.
The interview ended rather abruptly after King asked about immigration.
"Let's get something clear, because I've known you a long time," he said. "What are your feelings about Mexican immigrants? What in your gut do you feel about this?"
But Trump was silent.
"Donald, are you there?" King asked. "I don't know what happened there. We did not lose the connection, so something happened. But such is life in the big leagues."