The Redstones are playing hardball.

The ailing 93-year-old mogul Sumner M. Redstone and his daughter, Shari Redstone, on Thursday made their intentions for the future of their $40 billion media empire crystal clear: They are calling for the reunification of CBS and Viacom in an all-stock deal that would leave the family in control of the combined company.

The father-daughter duo outlined their plans for the proposed deal in a 251-word letter sent Thursday to the boards of CBS and Viacom, instructing the directors to consider combining the two media companies. While the Redstones encouraged “full and fair deliberation and negotiation” on the potential transaction, the subtext of the letter was that the family would determine the fate of the two companies and that it wanted those two companies to become one.

The Redstones left the directors of CBS and Viacom with few other options besides continuing as independently controlled entities. In the letter, the Redstones stated that they would not “accept or support” any acquisition by a third party of either CBS or Viacom. They also said they would not support a deal that would “result in National Amusements surrendering its controlling position in either company or not controlling the combined company.”

The blunt and public nature of the letter was not only a signal of Shari Redstone’s vision for the two companies but also a way to build momentum toward having them combined under the leadership of Leslie Moonves, the chief executive of CBS. Mr. Moonves, 67, has expressed doubt about a corporate reunion, and winning him over is crucial to the plan to combine them.