The smelter is currently expected to reopen imminently after a two-month shutdown. Justice Gyan Sudha Misra made no comment on the smelter's operations pending the next hearing.
The local pollution board in southern Tamil Nadu state, which had originally ordered the smelter to shut at the end of March after complaints of emissions, took the case to the top court after the National Green Tribunal ruled against it.
The Supreme Court first said on Friday that the next hearing would be on June 12 but Misra brought it forward following requests from counsels of the involved parties.
The smelter, run by Sterlite Industries, a unit of London-listed Vedanta, uses imported concentrates and produces 30,000 tonnes of refined copper a month, more than half of India's total production. Its closure has squeezed domestic copper supplies and boosted imports.