The company is mired in disputes with the governments of Tanzania and the Democratic Republic of Congo over law changes that raise taxes in the countries.
Mugabe to face legislators over his previous pronouncements that the state had been deprived of at least $15 billion in diamond revenue by mining companies.
Congo's state miner Gecamines is seeking to dissolve Kamoto Copper Company (KCC), blaming Glencore for high debts that have weighed on the mine for more than 10 years.
First Quantum said that Zambia's tax agency had demanded the taxes, saying they were on import duties, penalties and interest on consumables and spare parts.