The shares will be transferred to privatization authority AAAS.
Ponta said there is an investor interested in Remin and the company might restart activity. The debt-equity swap will be regulated through a Government emergency ordinance, he added.
Remin Baia Mare shut down in 2006, keeping only 300 employees for mine tunnel maintenance.
Before collective layoffs in 1996, the company employed some 14,000 people.
In 2006, the privatization authority said Remin Baia Mare had debts of $0.853 million.