Iceland plans to sell its remaining 65% stake in Islandsbanki in stages over the next two years, according to the country's state holding company.
Islandsbanki, formerly Glitnir, was one of three lenders that failed within days of each other in 2008, prompting a state takeover.
The state holding company, ISFI, said in a statement that it had formally submitted the sale proposal to the finance ministry in accordance with plans laid out in the 2022 budget.
The state sold off 35% of its ownership in Islandsbanki last year in the country's largest ever initial public offering.
This was a major step in reducing state ownership of the banking sector well over a decade after it imploded during the 2008 financial crisis.
The value of the bank has risen 30% since the June IPO, bringing its current market value to 250.2 billion Icelandic crowns ($1.95 billion).
The state holding company said it would only sell the stake if market conditions were favourable. Iceland plans to use part of the proceeds to fund infrastructure projects.
Islandsbanki has a domestic market share of around a third and around 740 employees.