Hospitals across California have continued to fill rapidly to dangerous levels as state and local officials try to dampen the explosive spread of the coronavirus in the state, Gov. Gavin Newsom said on Monday.

More than 10,000 Covid-19 patients are now hospitalized in the state, he said, 72 percent more than two weeks ago. The number in intensive care has risen by 69 percent over that time.

“You can see how quickly this grows,” he said at a news conference.

The nation’s most populous state tried to prepare for an autumn surge by readying emergency health care facilities, stockpiling thousands of ventilators, ramping up testing and other measures. Those preparations are now being tested on a vast scale by the deadly upward trajectory in the state’s case counts.

Starting Monday, millions of Californians are living under some of the most aggressive restrictions since March, when the state imposed the nation’s first stay-at-home order. Experts say that order helped to curb the spread of the virus in California at a time when it was raging out of control in places like New York City and hospitals there were swamped.

This time around, California’s new directives to stay home as much as possible in three of its five regions have run into much more resistance, even though the virus is more prevalent now than it has ever been. The sense of exhaustion and frustration is more palpable, as leaders beg weary residents to hold on through one more difficult stretch before vaccines are widely available.

Many people in the state say they’ve heeded the guidance about making their lives safer by moving activities outdoors and wearing masks, and that the new restrictions are sending a confusing message by closing playgrounds and barring people from gathering with relatives, even outdoors, while keeping shopping malls open.

On top of that, law enforcement leaders around the state, including Sheriff Don Barnes of Orange County, have said they will not enforce the new restrictions.

On Monday, after new restrictions went into effect in most of the state, Mr. Newsom sought to head off any panic about hospital capacity.

He said the state still had more than 73,000 open hospital beds, and that regional leaders have been gauging where to pull back on elective surgeries to preserve space for emergency patients. He discussed programs to bring on additional health care workers and to allow some patients in hard-hit areas to be treated at home with oxygen.

“I hope some of this will add more optimism to the frame,” he said.

Even so, state officials say that they expect the situation to worsen as the impact of Thanksgiving travel and gatherings becomes clearer.

“We know that cases that potentially occurred during Thanksgiving are going to show up right about now,” said Dr. Mark Ghaly, the California secretary of health and human services.

Mr. Newsom also announced the statewide rollout on Monday of a new app, developed in partnership with Google and Apple, that can notify users when they may have been exposed to someone who has tested positive for the virus. The technology relies on Bluetooth to detect which phones have been within several feet of one another for more than a few minutes, and can be challenging to get people to use, some experts have said.

The system is voluntary, and arrives more than nine months into a pandemic that has outrun all other efforts to alert people to potential exposure through contact tracing, leading to skepticism about how effective the app will prove to be.