(Adds other exit polls, background)

JERUSALEM, June 12 (Reuters) - Former Prime Minister Ehud Barak was leading a close race for the leadership of Israel's Labour Party on Tuesday, television exit polls showed.

Labour is the senior partner in the coalition of Prime Minister Ehud Olmert and its leader will hold a key post in the cabinet.

Three television channels put Barak ahead of challenger Ami Ayalon, but the margins left the race too close to call.

Channel 1 gave Barak the biggest victory margin of 52 percent compared to 48 percent for Ayalon, channel 10 had him leading by 51 percent against 49 percent for his opponent, while channel 2 put the margin at only 50.5 to 49.5 percent.

Barak and Ayalon, a retired navy admiral and security chief, went to a run-off after they beat the incumbent Labour head, Defence Minister Amir Peretz, in a first round last month.

Peretz has said he would resign as defence minister, potential freeing up the portfolio for the new Labour leader.

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