President Obama has proposed granting Israel the largest package of military aid ever provided by the United States to another nation, but he and Prime Minister Benjamin Netanyahu remain deeply at odds over a figure for the assistance despite months of negotiations. American officials have balked as their Israeli counterparts insisted on more generous terms for a new 10-year military aid package that could top $40 billion. The divide, which could have broad national security implications for both the United States and Israel, is exacerbated by the pent-up animosity between Mr. Obama and Mr. Netanyahu, which has been stoked by their radically divergent views of the nuclear deal with Iran. Israel has been the largest cumulative recipient of American foreign aid since World War II. Discussions about the agreement are being conducted in strict secrecy. Neither side would detail specific funding levels. But the disputes over money are grounded in more profound rifts over policy, politics and national security strategy. While the president views the Iran agreement as having bolstered Israel's security ... by restraining Tehran's ability to develop a nuclear weapon, the Israelis believe that the lifting of sanctions on Iran has only emboldened a government that directly threatens them. The administration doesn't want to lose the Iran battle after they've already won it by rewarding Israel with an over-the-top increase in aid," said Aaron David Miller, vice president of the Woodrow Wilson International Center for Scholars.