For weeks President Biden has emphasized that his goal for rolling out the coronavirus vaccine was an easy-to-remember 1 million shots a day, or 100 million vaccinations in his first 100 days. On Monday, he suggested a much faster clip, saying he could envision 1.5 million vaccinations per day.

“I think with the grace of God . . . we’ll be able to get that to 1.5 million a day,” Biden told reporters.

A million a day is still his minimum goal, Biden said, but “I hope we’ll be able to increase as we go along so we’ll get to 1.5 million. That’s my hope.”

The recalibration reflects the reality that the country is already close to the million-a-day pace, using procedures put in place by the Trump administration. Over the past few days, Biden’s nascent administration has faced criticism for setting an artificially low goal — though when it first made the pledge, circumstances were different and it seemed potentially hard to meet.

Overall, Biden on Monday projected a relatively optimistic timeline, even while acknowledging the death toll from covid-19 could eventually reach 600,000 or even 660,000. By spring, he said, everyone who wants a vaccine should be able to get one.

“It’s going to be a logistical challenge that exceeds anything we’ve ever tried in this country, but I think we can do that,” he said. “I feel confident that by summer we’re going to be well on our way to heading toward herd immunity. I feel good about where we’re going, and I think we can get it done.”

Curbing the virus, and improving distribution of the vaccine, was a cornerstone of Biden’s presidential campaign, while former president Donald Trump’s mishandling of the pandemic was a major reason for his loss. Democrats hammered at the idea that Trump, who contracted the coronavirus himself, had not even been able to keep himself safe, let alone other Americans.

Now, Biden’s aides believe his ability to deliver on the promise of containing the pandemic will be critical to his success and the only way to revive the struggling economy. Since taking office last week, Biden has sought to find a balance between promising that the virus can be vanquished and warning that dark days still lie ahead.

His comments Monday came during the first formal question-and-answer session of his presidency with reporters. Due to covid-19 restrictions only a handful of journalists, including one from The Washington Post, were allowed in the room with him. And rather than taking questions in the White House itself, the event took place in an auditorium in the adjacent Eisenhower Executive Office Building.

Biden also sought to define what he means by urging “unity,” a longtime slogan that has come under growing scrutiny since he’s taken office. Republicans say it must include more concessions on Biden’s part, while liberals question the notion of unifying with those who they say attacked democracy.

The president sought to provide a somewhat nuanced definition, describing a need to “eliminate the vitriol” in political discourse and suggesting that unity means respectful debate, not total agreement.

“We’re going to argue like hell — believe me, I know that,” Biden said. “But I think we can do it in a way that benefits the American people.”

For now, much of the political debate surrounds the pandemic and how best to address it and soften its economic consequences. Last week, as Biden was settling into the White House, critics argued that he was under-promising on his vaccination schedule, perhaps to make it easier to declare victory later.

Even with vaccine shortages and bottlenecks in delivery, the pace needed to meet Biden’s goal — 1 million doses administered per day — was achieved last Friday and on four other days of the previous eight, according to Washington Post data. The accelerating speed of the program also arguably undercut assertions by some Biden advisers that they were left no plan at all by the Trump administration.

When reporters noted this disparity last week, Biden pushed back, noting that when he first announced the million-a-day goal some experts said it was unrealistic. “When I announced it, you all said it’s not possible,” Biden said. “Come on, give me a break, man. It’s a good start.”

Scientists are still determining the virus’s herd immunity threshold for humans — that is, the percentage of the population that needs to be immune for the spread of the virus to slow and eventually stop. Estimates currently range from about 40 percent to 80 percent of the population.

Biden noted that over the weekend he’d directed the Federal Emergency Management Agency to help with some aspects of vaccine distribution in West Virginia. The new administration has promised to stand up 100 FEMA centers across the country where vaccinations will be available.

Separately, Biden said he will extend a ban on travelers from Brazil, the United Kingdom, Ireland and 26 other European countries that had been set to expire Tuesday under a proclamation signed by Trump shortly before he left office.

And he plans to impose new restrictions on those coming from countries where a new variant of the virus is spreading. He added travelers from South Africa to the list of those barred from entering the United States, a change set to take effect Saturday.

“With the pandemic worsening and more contagious variants spreading, this isn’t the time to be lifting restrictions on international travel,” White House spokeswoman Jen Psaki said during a news briefing on Monday. She said the decision was part of the administration’s “science-driven response” to the coronavirus.

The administration is also taking steps to require travelers to quarantine after their arrival in the United States and to be tested a second time. Details on how those measures will be implemented are expected in the coming days.

In an interview on “CBS This Morning,” Anthony S. Fauci, the government’s top infectious-disease expert, said extending the ban and including South Africa “clearly will be helpful.” He said it is prudent to restrict travel of non-U.S. citizens.

“We have concern about the mutation that’s in South Africa,” Fauci said. “It is clearly different and more ominous than the one in the U.K.”

Biden brushed aside predictions that his proposed $1.9 trillion covid relief package would be torpedoed by Republican objections, saying it is still too early in the process to tell whether the two sides can come together.

He said it will take several more weeks to determine whether Democrats have to resort to a parliamentary process called reconciliation, which allows bills to pass the Senate with a simple majority instead of 60 votes, he said.

“No one wants to give up on their position until there is no alternative,” Biden said. “I think we’re far from that point right now. The decision on reconciliation will depend on how this negotiation goes.”

In his early days, the president has been seeking to convey two ideas that may be difficult to reconcile — that his administration is wholly focused on the pandemic and throwing every resource at it, and also that it will take a long time to defeat it.

“I’m going to shut down the virus, but I never said I’d do it in two months,” Biden said Monday. “It took a long time to get here. It’s going take a long time to beat it.”

He noted that Monday deaths from covid have ticked down in the past few days. Still, he said he believes the country will see as many as 660,000 deaths “before we begin to turn the corner in a major way.”

“We will still be talking about this into the summer,” Biden said. “We’re still going to be dealing with this issue in the early fall.”

As he frequently does, Biden also took the opportunity to remind Americans to wear masks. He has requested that masks be worn for his first 100 days in office and ordered that everyone on federal land and federally controlled property be required to wear them.

Lori Aratani contributed to this report.