BRUSSELS—European powers won’t move to reimpose international sanctions on Iran and kill the 2015 nuclear deal as long as Tehran restrains expansion of its nuclear work, diplomats said, potentially increasing tensions with the Trump administration.

France, Britain and Germany last week triggered a dispute-settlement mechanism in the 2015 deal that could lead the European Union and the United Nations to reimpose sanctions on Iran within 60 days. The 2015 deal, which sought to constrain Iran’s nuclear capabilities, had suspended...