The certificates need to be from destination countries in order to claim tax refunds, the Zambia Revenue Authority (ZRA) said.
Finance minister Alexander Chikwanda said last month the tax authorities in Africa's second-biggest copper producer would suspend the requirement because it was impracticable.
He added that the government planned to negotiate a staggered repayment of 600 million US dollars in VAT paid by copper mining companies and other exporters and withheld because of failure to produce the import certificates.
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The ZRA said Value Added Tax (VAT) withheld before the waiver came into effect could only be refunded when the import certificates had been produced.
"ZRA is considerate of stakeholder concerns in the administration of taxes. Accordingly, ZRA has amended these rules," it said.
Last year, the government started enforcing a 2008 requirement that exporters provide certificates for copper shipments in order to curb tax avoidance.
The companies complained that they were often unable to do so because they sold via middlemen.
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The companies affected include the local units of First Quantum Minerals, Vedanta Resources, Barrick Gold and Glencore Xstrata.