NIAMEY, Niger — A crucial military relationship between the United States and its closest West African ally, the country of Niger, ruptured this spring after a visiting U.S. official made threats during last-ditch negotiations over whether American troops based there would be allowed to remain, according to the country’s prime minister. In an exclusive interview, Prime Minister Ali Mahaman Lamine Zeine put the blame for the breakdown squarely on the United States, accusing American officials of trying to dictate which countries Niger could partner with and failing to justify the U.S. troop presence, now scheduled to end in the coming...