Hungary and Turkey are the only two remaining NATO members to not yet have ratified the applications.
"All eyes are now on Hungary and Turkey. We are waiting for these countries to ratify our applications. I think it would be important that this would happen preferably sooner than later," Marin told a joint news conference with other Nordic leaders, Reuters reported.
Finland and Sweden last week reiterated they would join NATO at the same time, presenting a united front to Turkey.
The Nordic neighbours asked to join the NATO alliance in May in response to the Russia-Ukraine war, but ran into objections from Turkey which has accused the two of harbouring groups it deems terrorists.