The widow of Aleksei A. Navalny said on Monday that she would carry on her husband’s work to bring about a democratic and free Russia, presenting herself for the first time as a political force and calling on his followers to rally alongside her.

Mr. Navalny’s sudden death in prison, which was announced by the Russian authorities on Friday, left a vacuum in Russia’s opposition. His supporters had wondered whether his wife, Yulia Navalnaya — who long shunned the spotlight — might step in to fill the void.

In a video released on Monday, Ms. Navalnaya, 47, signaled that she would. She said she was appearing on her late husband’s YouTube channel for the first time to tell his followers that the most important thing that they could do to honor his legacy was “to fight more desperately and furiously than before.”

“I am going to continue the work of Aleksei Navalny and continue to fight for our country,” Ms. Navalnaya said. “I call on you to stand beside me, to share not only in the grief and endless pain that has enveloped us and won’t let go. I ask you to share my rage — to share my rage, anger and hatred of those who have dared to kill our future.”

The nearly nine-minute video was crafted as an introduction of sorts to a new leader of the pro-democracy movement against President Vladimir V. Putin. It comes at a time when those opposed to the Kremlin strongman, who have sought to unite, feel more dispirited than ever.