LONDON — Jacob Rees-Mogg, the leader of Britain’s House of Commons and a prominent ally of Prime Minister Boris Johnson, suggested this week that victims of the 2017 Grenfell Tower fire lacked the common sense to defy firefighters’ orders and flee the building, costing them their lives.

The comments, appearing to lay some blame for the 72 deaths on the people trapped in the flames, angered other lawmakers and shocked even critics who have grown used to Mr. Rees-Mogg’s flashes of aristocratic obliviousness. They also threatened to undercut the Conservative Party’s main election pitch — that it’s a party for working-class voters alienated from the Labour Party over Brexit — just as campaigning for the Dec. 12 vote gets underway.

Nicknamed “the honorable gentleman from the 18th century,” Mr. Rees-Mogg was recently seen reclining on the front bench of the House of Commons, making clear his boredom during a fierce Brexit debate. And lawmakers said that a speech he gave in the run-up to a crunch vote was so arrogant that it persuaded members of his own Conservative Party to change their minds and rebuff the government’s Brexit plans.

Mr. Johnson, who is about to formally launch the Conservative campaign, is already saddled with a reputation for being haughty and occasionally out of touch. For a government trying to dispel an image of being a bunch of smug, entitled private-school types sleepwalking into national crisis, Mr. Rees-Mogg’s air of condescension and disdain has not been helpful.

But his comments this week threatened to be even more damaging, casting a fire widely seen as a failure of government oversight as, instead, the fault of the public housing residents who lost their lives in it.

A 900-page, government-commissioned report on the fire last week found that more people would have survived if firefighters had not told them to stay inside their apartments. Emergency operators also told residents to shelter in place, because the building was designed to stop the spread of fire.

Some tried to escape but were turned back by choking smoke, and others, not knowing where the fire was, feared that they would be walking into even more peril. Still others were physically unable to flee.

“If you just ignore what you’re told and leave, you are so much safer,” Mr. Rees-Mogg said on Monday in an interview with Nick Ferrari, the host of a show on LBC, a radio station. “And I think if either of us were in a fire, whatever the fire brigade said, we would leave the burning building. It just seems the common sense thing to do. And it is such a tragedy that didn’t happen.”

Late Tuesday morning, Mr. Rees-Mogg apologized, saying, “I would hate to upset the people of Grenfell if I was unclear in my comments.”

But some colleagues doubled down, with a Conservative lawmaker, Andrew Bridgen, suggesting that residents of Grenfell Tower exhibited a kind of deference common in people who were not fit, as Mr. Rees-Mogg was, to run the country.

“Jacob is a leader, he’s an authority figure,” Mr. Bridgen said in a radio interview, describing why Mr. Rees-Mogg would have made it out of the Grenfell fire alive. “We want very clever people running the country, don’t we?”

Opposition lawmakers and Grenfell survivors reacted furiously to Mr. Rees-Mogg’s remarks. Jeremy Corbyn, the opposition Labour leader, called them “crass” and “insensitive.”

“What possesses someone to react to an entirely avoidable tragedy like Grenfell by saying the victims lacked common sense?” Mr. Corbyn wrote on Twitter. “People were terrified, many died trying to escape.”

Ahmed Chellat, who lost five relatives in the fire, told the newspaper the Mirror: “What common sense is he talking about? People died on the stairs trying to leave, they couldn’t breathe. People needed help and directions, they tried to open doors and there was smoke everywhere.”

Mr. Rees-Mogg’s double-breasted suits, antique diction and penchant for polysyllabic words have long endeared him to a nostalgic set of Conservatives pining for the return of a different Britain. He has opposed climate change legislation, same-sex marriage, large-scale immigration and increased spending on social services, while supporting corporate tax cuts.

As a lawmaker with impeccable pro-Brexit bona fides and a wide following on the right wing of the party, he is among the most prominent cabinet ministers in Mr. Johnson’s government.

But Mr. Rees-Mogg’s unabashed elitism and past support for a no-deal Brexit that economists say would do serious harm have made him a frequent target of critics who would like to make him, not Mr. Johnson, the emblem of the government.

An Oxford graduate who named his sixth child Sixtus, Mr. Rees-Mogg recently had his wife’s ancestral home benefit from a state-funded restoration at a cost of 7.6 million pounds, about $9.8 million. He is a partner in an investment firm that has been criticized for operating in overseas tax havens.

His remarks on Grenfell were the second time in days that his party found itself in hot water over the disaster. Last week, during a debate in the House of Commons over the release of the government report, Mr. Corbyn wore a bright green tie, a color long used to honor victims of the fire.

Conservative lawmakers treated it as a fashion blunder and laughed at Mr. Corbyn, eliciting an angry response from Theresa May, Mr. Johnson’s predecessor, who had to remind her colleagues that it was for Grenfell.