The government is pressing for the liquidation of KCM which it has accused of breaching its operating licence. The company faces a lawsuit in the English courts over allegations KCM polluted the land of nearly 2,000 Zambian villagers.
KCM's Zambian business consists of three mines and a refinery and produced 195,300 tonnes of copper in the year to March 2018, KCM's annual report showed.
Friday's hearing was adjourned because Vedanta had not served documents, Jonas Zimba, the lawyer for KCM's appointed liquidator, told reporters.
Vedanta lawyer Michael Mundashi declined to comment.
Vedanta is seeking to be part of the KCM liquidation proceedings from which it has been excluded.
Vedanta has "serious concerns about the intentions of the applicants and the procedures that were followed by ZCCM-IH as a representative of the government to obtain a provisional liquidation order," it said in a statement on Thursday, adding it would fully defend its legal rights.
Zambian firm ZCCM-IH holds around 20 percent while Vedanta Resources, part owner of the Mumbai-listed Vedanta group of companies, holds a majority stake.
Vedanta said the petition for winding up KCM dealt with a "broad range of issues relating to KCM not at all related to the solvency of the business".
The company also said a number of expatriate employees and contractors had been prevented from leaving the country.
Zambia has riled miners with tax changes they say will force them to withhold the investment Zambia needs.
Moody's on Thursday downgraded Zambia's credit rating, citing liquidity pressures that have impaired the government's ability to service its debt.
Zambia's kwacha currency has weakened by more than 6 percent against the dollar this year and analysts expect it to come under further pressure as investor confidence erodes.
Vedanta says it is owed more than $180 million in value-added tax refunds from the government.
The government has said it will repay legitimate refunds but is seeking to introduce a sales tax that would not be refundable.
One of Zambia's biggest taxpayers First Quantum had threatened to lay off workers because of the new taxes, but later said it had abandoned those plans and was in talks with the government.
Glencore has said it will close two mine shafts because they have reached the end of their economic life. Union leaders have urged Glencore to reverse that decision.
Nick Branson, senior Africa analyst at Verisk Maplecroft, said in a note that Zambian President Edgar Lungu's "aggressive targeting of global commodity firms" hinted at Zambia's increasing reliance on China, its largest bilateral creditor.
"Extensive borrowing from Beijing has largely shielded Chinese mining companies from encroachment, while exposing others to greater pressure," he said.
(Reporting by Chris Mfula in Lusaka, Barbara Lewis in Johannesburg; additional reporting by Karin Strohecker in London; editing by David Goodman and Jason Neely)
By Chris Mfula and Barbara Lewis