TEL AVIV—Israeli Prime Minister Benjamin Netanyahu faces rising pressure from members of his government, including within his own Likud party, to reject any compromise with the U.S. and the Palestinians to extend a building moratorium in the West Bank.

A partial moratorium on West Bank settlement construction expires next month, just weeks after direct Israeli-Palestinian peace talks are set to begin in Washington next week. The Palestinians have said they won't engage in talks if an extension isn't...