Eleven of the animals were killed in Hwange National Park, the same park where Cecil the lion lived prior to his death earlier this year.
The announcement was welcomed by conservationists, who, citing its detrimental impact on wildlife, have long been pushing for an all-out ban.
The 13 adults and 12 pups were found on an isolated beach near Cape Lisburne.
The animal, which patrolled Indonesia's jungles to help protect threatened habitats, has been killed for his tusks.
In three years, and in spite of efforts to stop the slaughter, more than 100,000 elephants were killed for their ivory. What stands in the way of ending illegal poaching?
More than two tons of ivory were crushed, in a country renowned for being a hub for illegal tusks.
Hundreds of rare rhinos and other animals are fleeing flooding in India's northeast, raising fears of a rise in poaching during the exodus.
The female rhino was attacked by poachers, who removed one of its horns and also killed the rhino's baby.
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