Israeli Prime Minister Benjamin Netanyahu challenged President Obama on Thursday to reaffirm U.S. commitments to allow Israel to keep major settlements in the West Bank as part of any final peace deal with the Palestinian Authority.

The Israeli leader made the request ahead of his White House visit Friday and an hour after Mr. Obama delivered his major speech on the Middle East in which he said Israel’s 1967 border should be the basis for negotiating the borders of a Palestinian state.

After Mr. Obama’s speech, Palestinian Authority President Mahmoud Abbas called an emergency meeting of Palestinian leaders...