Representative Nancy Pelosi, Democrat of California and the former House speaker, on Sunday called for the F.B.I. to investigate protesters demanding a cease-fire in the Israel-Hamas conflict, suggesting without evidence that some activists may have ties to Russia and President Vladimir V. Putin.

“For them to call for a cease-fire is Mr. Putin’s message,” Ms. Pelosi said during an interview on CNN’s “State of the Union.” “Make no mistake, this is directly connected to what he would like to see. Same thing with Ukraine. It’s about Putin’s message. I think some of these protesters are spontaneous and organic and sincere. Some, I think, are connected to Russia.”

When pressed on whether she believed some of the demonstrators were “Russian plants,” Ms. Pelosi said: “Seeds or plants. I think some financing should be investigated. And I want to ask the F.B.I. to investigate that.”

Ms. Pelosi, who was first elected speaker in 2007 and again in 2019, led House Democrats for 20 years before stepping aside for Representative Hakeem Jeffries of New York, the minority leader. Still, she remains influential among congressional Democrats. Her remarks appear to be the first time a prominent U.S. politician has publicly suggested Russia may be backing cease-fire protests to help foment division among Democrats.

The Council on American-Islamic Relations condemned Ms. Pelosi’s comments as “an unsubstantiated smear” and “downright authoritarian.”

“Her comments once again show the negative impact of decades of dehumanization of the Palestinian people by those supporting Israeli apartheid,” Nihad Awad, the group’s national executive director, said in a statement. “Instead of baselessly smearing those Americans as Russian collaborators, former House Speaker Pelosi and other political leaders should respect the will of the American people by calling for an end to the Netanyahu government’s genocidal war on the people of Gaza.”