WASHINGTON—Jordan is in advanced talks with the Obama administration to conclude a civilian nuclear-cooperation agreement with the U.S., according to Jordanian and U.S. officials. Successful completion of the negotiations would make Jordan the second Arab state in less than a year, following the United Arab Emirates, to secure nuclear assistance from Washington. Any pact would constitute an international treaty and need the approval of Congress. The talks come as Iran is accelerating its production of nuclear fuel, raising the prospect of an expanding nuclear-arms race in the Middle East. An accord with King Abdullah II's government in Amman would allow...