Spin. Pilates. Prigozhin? Presidential Business Follows Biden on Vacation.

On Thursday, from a sprawling mansion on Lake Tahoe, President Biden spoke with President Volodymyr Zelensky of Ukraine, commemorating the country’s Independence Day and discussing the commencement of training its military fighter pilots.

On Wednesday, by the time Mr. Biden joined his family for a Pilates class, he had signed a disaster declaration to help Alaska recover from historic flooding, gotten word of an active shooter in Pittsburgh, and been briefed on reports that the mercenary leader Yevgeny V. Prigozhin had died in a plane crash in Russia.

And on Monday, he flew to Hawaii to tour a coastal town that had been scorched by deadly wildfires. Mr. Biden met with hundreds of grieving residents on the one-day trip, which included 10 hours of flying and two helicopter rides.

Mr. Biden’s weeklong vacation to Lake Tahoe, where he has been staying at a home owned by Tom Steyer, the billionaire climate investor, has been punctuated by moments of crisis at home and abroad.

It is a dynamic that seems to come with the job: A crisis will almost certainly unfold during any presidential holiday.

The only occasion when Mr. Biden was spotted doing a recreational activity so far was on Wednesday, holding a banana-blueberry smoothie after his workout at PeloDog, a Pilates and cycle studio. He was asked by reporters whether he believed President Vladimir V. Putin of Russia was behind the plane crash. It looked that way, the president said, but he needed to find out more.

“I’ve been working out for the last hour and a half,” he said.

Mr. Biden’s aides say the president values family time, but there was neither hesitation nor perceived sacrifice in traveling to Maui, which coincided with other brewing natural disasters. And for the most part, the president and his family have retreated to Mr. Steyer’s lake-view home in the gated community of Glenbrook, Nev., the oldest settlement in Lake Tahoe with one of the most expensive ZIP codes in the country. (White House officials said the president was renting the house for “fair market value” but did not disclose details.)

And observers say that Mr. Biden seems to have embraced the reality that has become inevitable for most presidents since Theodore Roosevelt installed a phone at his home in Sagamore Hill, on Long Island, to work during the summers.

“When you’re president, things are constantly coming your way — there’s no respite,” said Tevi Troy, a presidential scholar and former George W. Bush administration official, who wrote the book “Shall We Wake the President?” “So you can say that August is a nice time to take a vacation — go to Tahoe, or Rehoboth or wherever it is you like to — but this just doesn’t leave you.”

President George H.W. Bush was vacationing in Kennebunkport, Maine, in August 1991 amid an attempted Soviet coup; in August 1998, President Bill Clinton announced airstrikes in Afghanistan and Sudan from Martha’s Vineyard.

But the public perception of a president’s relaxing holiday can backfire.

Mr. Biden has come under criticism from Republicans for not saying enough publicly, in their view, about the Maui wildfires before his visit. White House officials said he had signed the major disaster declaration, which would deploy federal relief, within 63 minutes of its arriving at the White House, and had been on the phone and in briefings about the inferno every day during a vacation in Rehoboth Beach, Del., that weekend.

On Thursday, a White House spokeswoman said that Mr. Biden had never heard a reporter’s question about the fires in Maui that he appeared to brush off with a “no comment” on Aug. 13 in Delaware.

In 2002, George W. Bush was in an early morning golf game in Kennebunkport when he took time to condemn a deadly suicide bombing of a bus in Israel. “I call upon all nations to do everything they can to stop these terrorist killers,” Mr. Bush said on the first hole of Cape Arundel, at 6:15 a.m. “Thank you,” he said before immediately turning back to his game. “Now watch this drive.”

The younger Mr. Bush was also criticized for not returning from vacation at his ranch in Crawford, Texas, until days after Hurricane Katrina made landfall in August 2005.

In August 2014, President Obama faced criticism for continuing his golf game on Martha’s Vineyard just minutes after issuing a statement that “the entire world is appalled,” by the beheading of American journalist James Foley by Islamist extremists.

Advisers said the first few days of Mr. Biden’s vacation at Lake Tahoe provided a snapshot into an extraordinary convergence of crises facing the country — extreme weather, a war raging overseas and gun violence at home.

And historians say it also points to the increased expectations that presidents are personally responsible for the nation’s woes.

“I imagine there are 1,001 things that you and I could think of that a president of the United States could do to address climate change,” said Jeffrey A. Engel, the founding director of the Center for Presidential History at Southern Methodist University. “None of them involves grabbing a hose and watering down a building in Maui.”

On Wednesday, after balancing Pilates and Prigozhin, Mr. Biden went back to his 4,000-square-foot rental home tucked among the trees. And while his aides did not give much detail about what he was doing, it was not totally free of work: Mr. Biden said he would watch the Republican primary debate Wednesday night.

On the social media platform X, formerly known as Twitter, the @JoeBiden account posted a message just minutes after candidates wrangled over whether they believed in climate change: “Climate change is real, by the way,” the message said.