user10397: In a last round tie between 2 players fighting for top seed in a competition, here is what happened.
White had 18 seconds on his clock and black had 26 seconds. Black was winning. At move 56, black made a pawn push which exposed his king to a check by a dark square bishop, thus making the pawn push an illegal move. White did not take note so he  raised the bishop and was about to play then he saw that the king was in check, so before he could call 'illegal' black quickly called the 'touch move rule'. Thus implying that white had to move the bishop. According to FIDE rules which call should supersede: Black's 'touch move' or white's 'illegal move'?

user9684: From FIDE's Laws of Chess
7.5 

a. If during a game it is found that an illegal move has been
  completed, the position immediately before the irregularity shall be
  reinstated. If the position immediately before the irregularity cannot
  be determined, the game shall continue from the last identifiable
  position prior to the irregularity. Articles 4.3 and 4.7 apply to the
  move replacing the illegal move. The game shall then continue from
  this reinstated position.  If the player has moved a pawn to the
  furthest distant rank, pressed the clock, but not replaced the pawn
  with a new piece, the move is illegal. The pawn shall be replaced by a
  queen of the same colour as the pawn.
b. After the action taken under Article 7.5.a, for the first completed
  illegal move by a player the arbiter shall give two minutes extra time
  to his opponent; for the second completed illegal move by the same
  player the arbiter shall declare the game lost by this player.
  However, the game is drawn if the position is such that the opponent
  cannot checkmate the player’s king by any possible series of legal
  moves.

Since the illegal move reverts the position back to before the "touch move" would be activated, White never touched the Bishop.

user4418: In standard play (each player has at least 60 minutes for all the moves) it makes no difference when the illegal moves is spotted the position must be restored to the one before the illegal move even if that was several moves ago.
In rapid or blitz Appendix A4 part 2b applies:

b. An illegal move is completed once the player has pressed his clock.
  If the arbiter observes this he shall declare the game lost by the
  player, provided the opponent has not made his next move. If the
  arbiter does not intervene, the opponent is entitled to claim a win,
  provided the opponent has not made his next move.

Provided white has not released the bishop on a different square the claim for an illegal move stands and white wins the game.
EDIT: As of 1st January 2018 the rules for rapid and blitz have been brought into line with standard rate. In all 3 cases there is a time penalty for the first illegal move (1 minute for blitz and rapid, 2 minutes for standard) and only the second illegal move loses you the game.

10397: <p>In a last round tie between 2 players fighting for top seed in a competition, here is what happened.</p>

<p>White had 18 seconds on his clock and black had 26 seconds. Black was winning. At move 56, black made a pawn push which exposed his king to a check by a dark square bishop, thus making the pawn push an illegal move. White did not take note so he  raised the bishop and was about to play then he saw that the king was in check, so before he could call 'illegal' black quickly called the 'touch move rule'. Thus implying that white had to move the bishop. According to FIDE rules which call should supersede: Black's 'touch move' or white's 'illegal move'?</p>
 9684: <p>From <a href="http://www.fide.com/component/handbook/?view=article&amp;id=171" rel="nofollow">FIDE's Laws of Chess</a>
7.5 </p>

<blockquote>
  <p>a. If during a game it is found that an illegal move has been
  completed, the position immediately before the irregularity shall be
  reinstated. If the position immediately before the irregularity cannot
  be determined, the game shall continue from the last identifiable
  position prior to the irregularity. Articles 4.3 and 4.7 apply to the
  move replacing the illegal move. The game shall then continue from
  this reinstated position.  If the player has moved a pawn to the
  furthest distant rank, pressed the clock, but not replaced the pawn
  with a new piece, the move is illegal. The pawn shall be replaced by a
  queen of the same colour as the pawn.</p>
  
  <p>b. After the action taken under Article 7.5.a, for the first completed
  illegal move by a player the arbiter shall give two minutes extra time
  to his opponent; for the second completed illegal move by the same
  player the arbiter shall declare the game lost by this player.
  However, the game is drawn if the position is such that the opponent
  cannot checkmate the player’s king by any possible series of legal
  moves.</p>
</blockquote>

<p>Since the illegal move reverts the position back to before the "touch move" would be activated, White never touched the Bishop.</p>
 4418: <p>In standard play (each player has at least 60 minutes for all the moves) it makes no difference when the illegal moves is spotted the position must be restored to the one before the illegal move even if that was several moves ago.</p>

<p>In rapid or blitz Appendix A4 part 2b applies:</p>

<blockquote>
  <p>b. An illegal move is completed once the player has pressed his clock.
  If the arbiter observes this he shall declare the game lost by the
  player, provided the opponent has not made his next move. If the
  arbiter does not intervene, the opponent is entitled to claim a win,
  provided the opponent has not made his next move.</p>
</blockquote>

<p>Provided white has not released the bishop on a different square the claim for an illegal move stands and white wins the game.</p>

<p>EDIT: As of 1st January 2018 the rules for rapid and blitz have been brought into line with standard rate. In all 3 cases there is a time penalty for the first illegal move (1 minute for blitz and rapid, 2 minutes for standard) and only the second illegal move loses you the game.</p>
