VIENNA—A new U.S. and European-led push to censure Iran before the United Nations nuclear agency for alleged efforts to develop atomic weapons is facing resistance from Russia, China and a bloc of developing countries, which threaten to dilute any international punishment.

American and European officials on Wednesday said they believed they would reach an agreement with Beijing and Moscow on a resolution condemning Tehran's nuclear work, which will be presented to the International Atomic Energy Agency's 35-nation board of...