Polyus said in April it was buying back one group of notes because of volatility in the Russian markets caused by US sanctions.
Suleiman Kerimov, whose family controls the company, was among the oligarchs sanctioned over their links to the Kremlin.
This new buy back is much larger, covering bonds due 2020, 2022, 2023 and 2024, at a maximum cost of $300 million.
JP Morgan and DF King are running a modified Dutch auction for the notes.
Polyus produced 1.1 million ounces of gold in the first half of 2018, making a $358 million profit.
