The Trump administration on Friday claimed “remarkable progress” in fighting the coronavirus pandemic, despite a surge of cases in the South and West and as several Republican governors allied with President Trump are under pressure to impose stricter public health restrictions to gain control of outbreaks in their states.

Vice President Pence held the first public briefing of the coronavirus task force in nearly two months and sought to deliver an upbeat message that was at odds with warnings from public health experts. The vice president dodged the question of whether people should wear masks in public, as his own administration recommends, and said campaign rallies that pack people together, in violation of public health guidance, will continue.

Pence offered no new strategies to combat the rapidly spreading virus and minimized record daily case counts in several states as “outbreaks in specific counties.”

“As we stand here today, all 50 states and territories across the country are opening up, and safely and responsibly,” Pence said, a point that was undermined as Florida and Texas on Friday began to scale back or reverse their reopening plans because of growing outbreaks.

Pence’s remarks came as the virus has emerged as an urgent political crisis for Trump. With less than five months until Election Day, a slate of recent public opinion polls show Trump trailing former vice president Joe Biden, the presumptive Democratic nominee, both nationally and in several key battleground states, with voters taking a negative view of how the administration has handled the pandemic. Some of those states — including Arizona, Florida and Texas — are putting their reopening plans on hold.

The briefing was the latest effort by Pence and Trump to cherry-pick data as they attempt to gloss over the fact that on their watch, the United States has failed to stop the spread of a virus that the White House has often said will soon go away or have less and less impact on daily life.

While Pence acknowledged the rising numbers of cases in the South and the West, he sought to play down the threat while heaping praise on Trump for how he has handled the pandemic. The vice president argued that many of the new cases are being found in younger Americans, who are at less risk of developing deadly complications from the virus than older Americans are. He also argued that states have told him they have enough medical equipment to deal with the surge in infections and repeated the misleading claim that more testing is the main reason for the rising numbers of cases.

Pence rejected the idea that campaign rallies should be curtailed during the pandemic, arguing that the events are constitutionally protected free speech, and he defended two events Trump held in the past week over objections from local officials or the advice of his own public health advisers.

“Well, the freedom of speech, the right to peaceably assemble, is enshrined in the Constitution of the United States, and we have an election coming up this fall,” Pence said, adding that people who attend such events are offered screenings and health advice.

In a further sign of worry about the spread of the virus in the United States, Europe is poised to stop allowing American travelers into the European Union as it tries to permit more flights into E.U. member countries.

Trump has pushed for a swift reopening of shuttered businesses and an end to restrictions that have kept most people at home. In recent days he has reiterated that the economy will not be shut down again to contain the virus and has called outbreaks “embers” that can be put out.

Trump did not attend the briefing, which, unlike similar presentations early in the pandemic, was not held at the White House. Those sessions were discontinued as Trump sought to reduce the focus on the pandemic and move on, arguing that the economic toll of restrictions was too high.

The vice president and top federal public health officials spoke on the same day that Florida reported nearly 9,000 new coronavirus cases and announced that bars must close immediately, a move echoed in Texas, which is also dealing with a surge in cases and nearing its capacity to care for the infected.

Pence acknowledged that cases have been rising “precipitously” in some states, largely in the South, and announced that he and other task force officials would travel to Texas, Arizona and Florida in the coming days for on-the-ground reports.

He and federal health officials said the onus is on Americans to act responsibly and heed the advice of their local and state leaders, since conditions and risks differ across the nation.

Anthony S. Fauci, who leads the government’s infectious-disease effort, pleaded with Americans to take the virus seriously and continue exercising precautions some four months into a national state of partial paralysis.

“We are all in it together, and the only way we’re going to end it is by ending it together,” Fauci said.

He and other officials wore masks as they flanked Pence, who did not wear one. Fauci and the others removed their masks when speaking at the lectern.

Congressional Republicans have begun to express worries about the rising case numbers even as the White House has sought to downplay them.

House Minority Leader Kevin McCarthy (R-Calif.) suggested that nationwide protests against racial injustice were largely responsible for the spike that has led to record-setting numbers of new cases in recent days, despite a lack of evidence supporting such a connection.

Florida’s new-case report blew past the state’s previous single-day record of 5,511, set on Wednesday. It was the 19th day in a row that the state has hit a new average high. Average cases are now up about 77 percent from a week ago and 526 percent since Memorial Day.

The sharp increases are fueling concerns that Florida — where Gov. Ron DeSantis (R) has pushed an aggressive reopening strategy — is fast emerging as a new epicenter for the virus.

DeSantis has sought to blame the surging infections on farmworkers, anti-police-brutality protests and an increase in testing, while cheering on the relocation of the Republican National Convention to Florida.

The GOP announced in mid-June that it would relocate the celebratory public portions of its presidential nominating convention to Jacksonville, Fla., from Charlotte after Trump balked at North Carolina’s social distancing requirements.

The move has prompted growing concerns that a convention will only exacerbate the virus’s spread. According to data tracked by The Washington Post, cases in Duval County, which includes Jacksonville, have nearly doubled in the past two weeks.

Meanwhile, less than a day after announcing that Texas would pause reopening plans but not revert to stricter measures, Gov. Greg Abbott (R) issued an executive order that revives restrictions on bars, restaurants and certain types of outdoor recreation.

“The trajectory that we’re on right now has our hospitals being overwhelmed, probably about mid-July,” Austin Mayor Steve Adler (D) said during an appearance on CNN.

Nationwide, infections surpassed 40,000 for the first time Friday, the third national record this week.

Pence said the increases were being driven by people under age 35, which he called “very encouraging news” because they are generally less susceptible to severe illness from the virus.

Other countries are seeing total positive cases going down, regardless of age.

Pence dismissed the idea that premature reopenings by states had contributed to the recent outbreaks. He stressed that while cases have increased, the death rate has declined.

“This moment in the coronavirus pandemic is different than what we saw two months ago,” he said. “It’s almost inarguable that more testing is generating more cases. The volume of new cases is a reflection of the great success in expanding testing across the country.”

Health authorities, however, project that those younger people, many of whom show no symptoms, will probably spread infections to the more vulnerable. They warn of a lag time of about three weeks between when people are diagnosed and subsequent hospitalizations and deaths. They also note that while the death count has declined since the first wave of cases, it is slowly inching up as cases increase again.

Trump told rallygoers in Oklahoma on Saturday that he had asked officials to “slow the testing down, please” so the country would record fewer cases. White House officials have insisted that Trump made the comment in jest, but the president said this week that he wasn’t kidding.

Fauci, director of the National Institute of Allergy and Infectious Diseases and a member of the White House coronavirus task force, and other public health experts have said increased testing alone does not explain the recent increases.

Pence, when pressed by a reporter, declined to recommend that all Americans wear masks as public health officials advise, instead urging people to listen to their local health officials and pray. Deborah Birx, White House coronavirus response coordinator, urged everyone to wear a mask.

Trump refuses to wear a mask in public, calling it unpresidential, and the question has become increasingly partisan. Biden said this week that he would like mask-wearing to be mandatory.

House Speaker Nancy Pelosi (D-Calif.) criticized Trump for continuing to seek to kill the Affordable Care Act, even as coronavirus cases rise again, and for failing to model good practices by wearing a mask.

“So when the president of the United States says he doesn’t want to wear a mask and understands the bad example, well, I don’t know if he understands anything, but somebody over there must understand the bad example that is to the country,” she said.

John Wagner, Colby Itkowitz, Miriam Berger and Kim Bellware contributed to this report.