WASHINGTON—The leadership of the most powerful pro-Israel lobby in the U.S. publicly broke Sunday from the White House over the issue of Iran policy during the first of a three-day policy conference in Washington attended by 16,000 of its members.

Leaders of the American Israel Public Affairs Committee, or Aipac, outlined a strategy moving forward of working through Congress to disrupt any nuclear agreement with Tehran that is deemed too weak in denying the country a nuclear weapons capability.

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