In a nearly 90-minute phone conversation with Ms. Pelosi, Mr. Mnuchin reiterated his willingness to accept Democratic language with “minor” edits and said he would provide a proposal on Friday, Drew Hammill, a spokesman for Ms. Pelosi, said in a statement summarizing the conversation. “The speaker looks forward to reviewing.”

But a number of unresolved differences remain, such as how much money to provide to state and local governments and lapsed federal unemployment benefits.

Investors, who have been following the stimulus talks closely, seemed unmoved by statements from Mr. Trump and Mr. Mnuchin on Thursday, with stocks on Wall Street dropping for a third consecutive day. And Senate Republicans, who have grown increasingly frustrated with Mr. Mnuchin’s willingness to buck their narrow proposals and capitulate to Ms. Pelosi’s demands for a sweeping relief package, were equally reticent about the prospects of a deal before Nov. 3.

“I’m proposing what we think is appropriate,” Mr. McConnell said after voting in Louisville, Ky., when asked about the targeted bill he was preparing. At later events in the state, he noted that the administration had not yet successfully reached a deal and said he felt “it was important to indicate to the American people before the election — not after — that we were not in favor of a stalemate, that we were not in favor of doing nothing.”

Mr. McConnell, who has not formally unveiled legislation before an expected vote next week, said it would be similar to a scaled-down package that Senate Republicans proposed in September, which failed to meet the 60-vote threshold.

While some Democrats have pushed for Ms. Pelosi to accept a smaller relief package, she has insisted that the toll of the pandemic merits another broad package. With the original Democratic offer costing about $3.4 trillion, the speaker has repeatedly argued that she has been more than willing to compromise with her Republican counterparts, counseling Democrats in a private phone call on Tuesday that “I don’t think our leverage has ever been greater than it is now.”

“The disdain that they have for the state and local, the contempt that they have for science by not wanting to have a national strategic plan, and again, the unfairness when it comes to America’s workers, is a tough nut to crack.,” Ms. Pelosi said in an interview on MSNBC on Wednesday. “Still and all, we want to try and find our common ground.”

Masks are politically popular. They are embraced as a public health necessity by experts and a broad cross-section of the American public. One of Mr. Trump’s own advisers, Chris Christie, said Thursday he had been “wrong” not to wear a mask at the White House. But Mr. Trump, despite having recently contracted the coronavirus and requiring hospitalization for it, still cannot bring himself to arrive at a full-throated embrace of mask-wearing.

“I’m OK with masks — I tell people, ‘Wear masks,’” he said. But he couldn’t resist an addendum. “Just the other day,” he said, he had seen a study that showed that people using masks were still contracting the virus.

He tried to twist the position of Dr. Anthony S. Fauci, the nation’s foremost infectious disease expert, on masks. And he dismissed the scientific consensus.

“People with masks are catching it all the time,” he added.

It was exactly the kind of digression that has left Republicans frustrated: Six months, eight million cases and more than 215,000 deaths later, the president is still trying to bend the reality of the pandemic to his politics rather than the other way around.

The pandemic has upended American life like no other event, and death rates per capita are higher than in other developed nations, yet Mr. Trump continued to claim that his administration’s response had been a success. “We’re a winner,” Mr. Trump declared, talking about “excess mortality.” He added, “What we’ve done has been amazing, and we have done an amazing job.”

Biden finally addressed court packing — sort of.

Mr. Biden did make one bit of news: After energetically avoiding the question recently, he signaled that he would announce before Election Day whether he supports expanding the number of seats on the Supreme Court. But he said he wanted to wait until after the Senate had acted on the nomination of Judge Amy Coney Barrett to replace Justice Ruth Bader Ginsburg.

The weekly number of new coronavirus cases in Europe is now at its highest point since the start of the pandemic, a top World Health Organization official said on Thursday, urging governments to impose tighter, targeted controls on social gatherings.

The number of confirmed cases in Europe rose by a million to seven million in just 10 days, Hans Kluge, the WH.O.’s director for Europe, told reporters, and the number of daily deaths had passed the level of 1,000 for the first time in months. (An earlier version of this item stated incorrectly the last time daily deaths in Europe had passed 1,000; it was earlier this year, not ever.)

His warning came as Britain announced tightened restrictions on several areas, including London, where people from different households will be barred from meeting indoors starting after midnight on Friday. People will also be discouraged from using public transportation.

The new measures will also apply to the city of York, in northern England, as well as to parts of central and southeastern England.

Still, the military has repeatedly been singled out for human rights abuses and the use of excessive force, including accusations of extrajudicial killings that dogged the armed forces throughout General Cienfuegos’s tenure as defense minister.

But no high-ranking Mexican military official has been charged with money laundering and drug trafficking. Such charges would represent a new front in the effort to combat the corruption and extraordinary power wielded by organized crime in Mexico.

General Cienfuegos’s arrest does not appear to have been a joint operation with the Mexican government. The case against Mr. García Luna, the retired police official, was the direct result of testimony in the New York trial of the drug lord Joaquín Guzmán Loera, better known as El Chapo, who ran the Sinaloa cartel. It was unclear on Friday morning whether the arrest of General Cienfuegos was also related to the case against Mr. Guzmán, who was convicted in February 2019 after a three-month trial in Federal District Court in Brooklyn.

The Guzmán trial exposed the inner workings of his sprawling cartel, which over decades shipped tons of drugs into the United States and plagued Mexico with relentless bloodshed and corruption.

In 2016 and 2017, the years when Mr. Guzmán was arrested for a final time and sent to New York to be prosecuted — at a time when General Cienfuegos was defense minister — Mexican heroin production increased by 37 percent, and fentanyl seizures at the southwest border more than doubled, according to the Drug Enforcement Administration.

The D.E.A. noted as the case against Mr. Guzmán unfolded that the Sinaloa and Jalisco New Generation cartels “remain the greatest criminal drug threat” to the United States.

Prosecution of the Guzmán case was years in the making, and his trial drew upon investigative work by the F.B.I., the D.E.A., the United States Coast Guard, Homeland Security Investigations and federal prosecutors in Chicago, Miami, San Diego, Washington, New York and El Paso, Texas. The trial team also relied on scores of local American police officers and the authorities in Ecuador, Colombia and the Dominican Republic.