UNITED NATIONS—U.N. and European Union diplomats pushed back against U.S. criticism of Iran and declared Tehran to be in full compliance with its nuclear agreement in a Security Council meeting on Thursday.

U.N. Secretary-General Antonio Guterres praised Iran for its “full and effective” compliance in his third biannual report on the implementation of the nuclear deal, which was signed by Tehran and world powers in July 2015.

The...