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The stark warning was issued by the country's Environment Minister Edna Molewa on the sidelines of the Convention on International Trade in Endangered Species (CITES) in Bangkok.
"We think we will start to have problems around the year 2016," she said, adding 146 rhinos have been killed illegally since the start of the year with 50 suspected poachers arrested over the same period.
Some 668 rhinos were slaughtered in 2012, a grim record that on current trends will be surpassed this year.
The white rhino population is estimated at just over 18,000 and its birth rate is higher than mortality rates, according to Fundisile Mketani, an official from the nation's Department of the Environment.
But "with this (poaching) trend by 2016 - if we do not stop it - then we will see a decline", he added. "We will then be in crisis."
Rhinos are hunted for their horn, which is worth thousands of dollars in Asia where it is believed to have medicinal qualities.
They have been registered since 1977 under Appendix I of CITES, banning the trade in their parts and are one of the key species under scrutiny at the convention, along with African elephants whose numbers have been decimated over recent years.
Horns from the legal trophy hunting of white rhinos in South Africa and neighbouring Swaziland are exempt from the ban - a move some conservationists say has saved the species by encouraging game reserves to maintain large populations.
Kenya had submitted a proposal for a moratorium on the trophy trade, but withdrew it on Thursday.
Molewa "welcomed" the withdrawal of Kenya's proposal saying it would have ended the use of trophy hunting as a "management tool that can be sustainable and beneficial to the conservation of the species".
Source: AFP
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