Normally, just the words used in an oral threat would not be sufficient to be classed as assault. But when those words are coupled with some action that indicates the ability to carry out the threat, then that could be classed as assault.
So we have the situation that a mere threat to harm is not in itself an assault but a threat combined with a raised fist (or a waved baseball bat, or a gun pointed at your head!) might be sufficient if it causes a reasonable fear of harm in the victim