“I’m not going to hold on to this job,” he said, according to a report in the Página Siete newspaper. “I’m not going to put myself and my family at risk.”

Mr. Morales in his address cast himself as a victim of a conspiracy by people who “don’t respect democracy, and don’t respect the results of the last elections.” He called on the police to “uphold their duty to safeguard the safety of the Bolivian people.”

It was his strongest direct acknowledgment of the spreading rebellion.

He said the talks he was proposing should involve members of four parties that won legislative seats in the latest election, a criteria that would exclude some of the main leaders who have been mobilizing against him in recent days.

“We hope tonight to find peaceful solutions through dialogue,” the president said. “We’ll have an open agenda with the goal of pacifying Bolivia.”

Leaders of Bolivia’s main opposition parties swiftly rejected his proposal.

Mr. Morales also called on supporters to come out to defend his government, raising fears that clashes could intensify. On Saturday, eight anti-government protesters were injured when their convoy was ambushed by government allies on the way to a demonstration in La Paz, opposition leaders said.

Isabel Mercado, the director of Página Siete, one of the country’s main newspapers, said Saturday that Mr. Morales’s hold on power appeared to be slipping as the police mutiny grew and the leaders of the armed forces remained out of sight.

“Without the police and the armed forces, I think it’s very hard for him to hold on,” she said.

Local news media reported that police defections had spread to at least four cities outside La Paz. The police have demanded better working conditions, the resignation of their commander and guarantees they won’t be used for political ends, The Associated Press reported.