In an interview on Monday, Ms. Feinstein argued that the experience she brought to the job has been critical during turbulent times. She said voters would decide whether there was a need for new blood or ideology.

“I have the energy,” she said. “My mind is fine. I believe I will have strong support from Democrats — and from others.”

“I don’t think there is anybody that will say that they can’t work with me, that I haven’t been a hard worker, that I haven’t tried my level best to represent the needs of the state,” she said. “If somebody who is better gets elected, I say, ‘that’s fine.’”

In a poll released last month by the Public Policy Institute of California, 50 percent of likely voters surveyed said that Ms. Feinstein should not seek a sixth term. And there has been no shortage of speculation about potential challengers or successors: Mr. de Leon, who is barred from term limits from running for re-election, has signaled that he might run against her. He did not respond to a request for comment.

Shortly after Ms. Feinstein’s announcement, Markos Moulitsas, the founder of the Daily Kos, a liberal group that has proved to be a powerful fund-raising organization, encouraged Mr. de Leon to run. “We share a common interest in this Senate race,” he said on Twitter. “Let’s beat the most pro-Trump Blue-state Dem in the country!”

For all that, there are few political figures here who think that Ms. Feinstein is in major danger of losing re-election. She has been a fixture in California politics for nearly half a century, serving in the Senate, as the mayor of San Francisco and as a member of the county board of supervisors. “Not in the slightest,” said Dan Schnur, a longtime Republican strategist here. “No credible challenger would take the risk, which means the only possible challengers are by definition not credible.”