Mordachov has declined previous offers and is considered an ally of TUI boss Michael Frenzel and his strategy of selling the group's Hapag-Lloyd shipping unit to concentrate on tourism, where TUI is a European leader.
Fredriksen, who made a fortune in the container shipping sector, challenges such a move and demands that shareholders be consulted on the matter.
The Norwegian has proposed that each activity be run separately, with investors able to decide whether to back one or both units.
He has also called for Frenzel's resignation, noting that TUI has lost much of its value during his 14-year reign.