BRASÍLIA—Leading members of South America’s trade bloc Mercosur refused to allow Venezuela to take its turn as the group’s rotating leader and threatened to expel it from the organization over its failure to comply with trade and human rights bylaws.

Argentina, Brazil, Paraguay and Uruguay agreed late Tuesday to give the Venezuelan government a Dec. 1 deadline to meet Mercosur’s rules to qualify for the post. Meanwhile, the presidency will be filled by an interim team from the other member states, the four countries said in...