The oxygen production had to be stopped temporarily following a technical snag in the cold box at the oxygen plant on May 14.
In a statement shared on the micro-blogging site on Sunday, Sterlite Copper said, "efforts to resume production at our oxygen plant are progressing".
The plant was closed in 2018 after the Tamil Nadu Pollution Control Board (TNPCB) found violations of environmental norms.
Tamil Nadu: Madras High Court stays construction of new copper smelter by Sterlite industries in Thoothukudi
The stay comes a day after 11 people were killed and 20 others grievously injured after police reportedly opened fire multiple times against anti-Sterlite protesters in Thoothukudi on Tuesday.
'Ban Sterlite': Thousands of protesters hit the streets demanding closure of copper plant in Thoothukudi
Local residents argue that the existing smelter has been polluting their water and air since it was established in 1996.
British Tamils protest outside Vedanta chief Anil Agarwal's London home against Tuticorin Sterlite Copper Plant
Carrying traditional Tamil parai drums, dozens of protesters gathered outside the Mayfair home of the Vedanta chief to coincide with major demonstrations in Thoothukudi in Tamil Nadu yesterday.