Sumner Redstone's National Amusements, the majority shareholder of CBS Corp. and Viacom Inc.. on Thursday proposed a merger of the two and said it would not support the acquisition of either media company by a third party.

Privately held National Amusements said in a letter to both companies' boards that a merger would bring significant savings, but it would not support a transaction that would cause it to surrender control of CBS, Viacom or a combined entity.

CBS shares rose 3.1 percent to $55.82 in morning trading, while Viacom was up 1.1 percent at $36.97.

When Redstone split CBS from Viacom 10 years ago, investors saw the mainstream broadcaster as a slow-moving company catering to an older audience, compared with the young, scrappy Viacom, whose networks include Nickelodeon and MTV. But CBS shares have easily outperformed those of Viacom over the last five years.

Shari Redstone, Sumner Redstone's daughter and an owner of National Amusements, has been in favor of recombining the two under the leadership of CBS Chief Executive Officer Leslie Moonves, sources have previously told Reuters.

Reuters was the first to report on Wednesday that National Amusements could contact CBS and Viacom as soon as this week to ask them to form independent board committees to discuss a potential merger.

Industry speculation that the two might tie up has increased in recent weeks after the Redstones prevailed over a power struggle that resulted in the departure of Viacom Chief Executive Officer Philippe Dauman.

"We believe that a combination of CBS and Viacom might offer substantial synergies that would allow the combined company to respond even more aggressively and effectively to the challenges of the changing entertainment and media landscape," said the letter from National Amusements, which owns 80 percent of the voting shares of both companies.

Both companies acknowledged receipt of the letter.

CBS's management and independent directors "will take appropriate actions to evaluate what is in the best interest of the company and its shareholders," a spokesperson said.

Viacom said it expected its board to form a special committee of independent directors to consider National Amusements' request.

In its letter, National Amusements said the optimal deal would be an all-stock transaction giving holders of each company shares in the combined entity of the same class as they currently own.

Any transaction would require the approval of both boards. Sumner and Shari Redstone will not vote on the deal as directors of Viacom and CBS or participate in deliberations, according to the letter. David Andelman, a CBS director, will also not participate in the process.