Is taking the opponent's king an illegal move? In competition blitz games, making an illegal move and then pressing the clock forfeits the game if the opponent claims the illegal move as long as they do not make a new move, as a new move would void the previous illegal move according to FIDE blitz rules.

I've seen all kind of forfeits because of this reason in blitz games, including one player taking one of his own pawns.

However, the most common case for illegal moves is neglecting that the King is in check or unprotecting the King. In this case where the King is checked, if the opponent takes the exposed king and presses the clock, are they making a new illegal move, hence voiding the previous one?

I've been told that taking the King, even as a kind of "joke" to expose a previous illegal move, is an illegal move by itself, because the King cannot be taken, only mated. Is this true under FIDE rules?
Capturing the King is an illegal move according to FIDE.

Refer to Article 1.2 from the Laws of Chess


  The objective of each player is to place the opponent’s king ‘under
  attack’ in such a way that the opponent has no legal move. The player
  who achieves this goal is said to have ‘checkmated’ the opponent’s
  king and to have won the game. Leaving one’s own king under attack,
  exposing one’s own king to attack and also ’capturing’ the opponent’s
  king are not allowed. The opponent whose king has been checkmated has
  lost the game.