President Obama is stirring resentment over his refusal to interrupt his Martha’s Vineyard vacation to survey the Louisiana flood — the worst U.S. natural disaster since 2012 — while drawing comparisons to President George W. Bush’s hotly criticized response to Hurricane Katrina in the same state.

Homeland Security Secretary Jeh Johnson defended Mr. Obama at a press conference Thursday, insisting that the president is “closely monitoring” the situation but that he will not cut short his two-week breather in the tony Massachusetts resort.

“The president can’t be everywhere,” Mr. Johnson told reporters in Denham Springs, Louisiana.

Louisiana Gov. John Bel Edwards, a Democrat, backed him up, saying at the press conference that he is “not complaining in any way about our federal partnership.”

Even so, Mr. Obama’s lack of urgency is drawing unflattering parallels to the federal response in 2005, when Mr. Bush was branded as uncaring and even racist for not touching down during a flyover two days after Hurricane Katrina unleashed record destruction along the Gulf Coast.

Not only has Mr. Obama refused to cut short his golfing vacation, but he also has issued no public or written statements about the crisis, which has been dubbed the Louisiana Flood of 2016.

The Advocate newspaper in Baton Rouge opened the floodgates Thursday by urging Mr. Obama to cut his vacation short and bring badly needed attention to the disaster, which has claimed 13 lives and damaged 40,000 homes after a series of storms that unleashed nearly 3 feet of rain.

“Vacation or not, a hurting Louisiana needs you now, Mr. President,” said the headline.

“We’ve seen this story before in Louisiana, and we don’t deserve a sequel,” the editorial said. “In 2005, a flyover by a vacationing President George W. Bush became a symbol of official neglect for the victims of Hurricane Katrina. The current president was among those making political hay out of Bush’s aloofness.”

The newspaper noted that Mr. Obama did stray Monday from Martha’s Vineyard, described as a “playground for the posh and well-connected,” to attend a nearby fundraiser for Democratic presidential nominee Hillary Clinton.

“I think when you need presidential leadership, you need presidential leadership, and when you sign up to be president, you sign up for a 24/7 job,” Advocate Editor Peter Kovacs said on CNN.

The White House has approved a federal disaster declaration for 20 parishes after thunderstorms rolled across the state starting Aug. 5, followed by a low-pressure system that caused rivers to overflow and flood communities, including Baton Rouge and Lafayette.

Mr. Johnson visited a day after FEMA Administrator Craig Fugate toured the area, and Mr. Edwards and other state officials have been keeping the administration apprised of developments, according to the White House.

In the absence of a presidential visit, however, the disaster and subsequent relief effort have drawn little national attention, especially when competing in a packed news cycle with stories about the Rio Olympics and the presidential race.

“You have the Olympics, you’ve got the election,” Mr. Fugate said. “If you look at the national news, you’re probably on the third or fourth page. FEMA understands this is a very large disaster impacting tens of thousands of people. Regardless of what it may be getting in the national coverage, we know there has been a significant impact here in Louisiana.”

The dearth of coverage drew a heated response from The American Conservative’s Rod Dreher, who lives in Louisiana.

“Honest to God, what is wrong with you media people?” Mr. Dreher asked in a Tuesday post. “I know, everybody thinks what’s happening in their part of the world is the most important thing ever. I get that. But come on, these floods are of national historical importance in the United States of America. And you national media people may find this hard to believe, but south Louisiana is as much a part of America as is Queens, northern California, and Pennsylvania. We’re not friggin’ Bangladesh.”

On the left, Salon’s Sean Illing also decried the low media interest. “In Louisiana, there’s a gnawing sense that the national media seems wholly uninterested in this disaster. One listens in vain for a mention of floods amid the breathless coverage of Donald Trump and Hillary Clinton’s email testimony,” he said.

While the arrival of Mr. Obama would bring with it international attention, Mr. Edwards said Thursday that the timing for a presidential visit is bad given the security required.

“If you would remember a few weeks ago when the vice president came for the memorial of the police officers that were shot and killed — if you will recall the impact that had on the community with respect to closing down interstates, the security that was required, and all of the police officers locally that had to be taken from other duties,” said Mr. Edwards. “Quite frankly, that is not something I want to go through right now.”

Of course, the Bush White House also argued that a presidential visit and the related security and press accommodation headaches would divert the region’s resources, and this did nothing to sap the outcry. On Sept. 2, two days after the flyover, Mr. Bush was on the ground meeting with victims in Biloxi, Mississippi, and other disaster sites.

“They created a crisis atmosphere and said, ‘Look at how Bush is failing,’ whereas with Obama, there is no crisis atmosphere,” said Tim Graham, the conservative Media Research Center’s director of media analysis. “There’s no atmosphere where we’re going to judge how he’s doing. He’s not involved. He’s not part of this story. And that’s kind of what I’m seeing.”

Not so on conservative websites and talk radio, where Mr. Obama has been reamed for golfing through the crisis.

“Where’s Obama? Where is he? I know. He’s up in Martha’s Vineyard and he’s playing his record whatever-number round of golf as president. It’s over 300 rounds now. Can’t be bothered,” said conservative talk show host Rush Limbaugh.

“Remember all the grief Bush got for flying over New Orleans and not landing there? Remember the grief Bush got when all he did was fly over in Air Force One? Obama hadn’t even gone, he hadn’t even made any pretense,” Mr. Limbaugh said.

The crisis isn’t over: More rain is expected, and about 4,000 people remain in shelters, down from about 11,000. More than 85,000 people have applied for FEMA assistance.

The Red Cross, which brought in hundreds of relief workers, has declared the Louisiana flood the worst disaster since Superstorm Sandy in 2012, which devastated the Eastern Seaboard.

Still, Hurricane Katrina was a far larger disaster in terms of scale and loss of life, prompting more than 60,000 rescues, versus about 30,000 so far with the Louisiana Flood. The Category 5 hurricane, which made landfall Aug. 29 on the Gulf Coast, claimed 1,836 lives.

The financial impact from the Louisiana Flood could be outsized because many of the damaged homes are inland and their owners have no flood insurance.

• This article is based in part on wire service reports from Louisiana.

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