Cruz was responding to Obama's recent criticism of Republicans suggesting there be a religious test for Syrian refugees seeking entrance to the country, a plan he called "shameful" and "not American" while in Turkey for the Group of 20 summit.
"If you want to insult me, you can do it overseas, you can do it in Turkey, you can do it in foreign countries. But I would encourage you, Mr. President, come back and insult me to my face," Cruz said, staring directly into the camera.
Cruz got even more schoolyard, challenging the President to a debate any place, any time.
"Let's have a debate on Syrian refugees, right now. We can do it anywhere you want. I would prefer it in the United States and not overseas," the Republican presidential candidate said. "We'll do it on any station."
Cruz also called Obama's remarks "utterly unfitting of a President."
Watch Cruz's full remarks, via NBC News:
This story has been updated.