President Biden on Thursday marked the 50 millionth coronavirus vaccine administered in the United States by urging the nation to stay vigilant as he defended the sometimes rocky rollout of his vaccine initiative, saying he was well into “cleaning the mess left us” by his predecessor.

The halfway mark to Biden’s stated goal of 100 million vaccines in his first 100 days comes just after one month into his presidency, a faster pace than the administration had first publicly set. But Biden also cautioned against complacency and told Americans not to let down their guard.

“At first, critics said that goal was too ambitious, no one could do that. Then they said it was too small,” Biden said of his 100 million shots promise. “Today, I’m here to report, we’re halfway there . . . That’s weeks ahead of schedule, even with the setbacks we faced in the recent winter storms.”

Still, the pace of a million vaccines a day had almost been reached by the time Biden took office, making his promise less far-reaching than it at first appeared.

The Trump administration, Biden asserted, left him with no broad strategy to vaccinate every American. He noted that the 12 million shots administered during this week were double the 6 million shots in President Donald Trump’s last week in office.

The task of vaccinating millions of Americans, Biden said, is the “greatest operational challenge this country has ever undertaken.” He added that his administration has worked to boost the number of people available to administer the doses, including by bringing doctors and nurses out of retirement. His team, Biden said, also has “fixed the problem” of the supply of vaccines.

He repeated multiple times that he was not taking a “victory lap” on Thursday. That reflected the sober and somber tone toward the pandemic that Biden and his aides have taken since the start of his presidency, despite some recent good news that suggests the spread of the virus in the United States was slowing somewhat.

“Covid cases and hospitalizations are coming down, but I need to be honest with you: Cases and hospitalizations could go back up with the new variants as they emerge,” Biden said. “This is not a time to relax. We must keep washing our hands, stay socially distant and for God’s sake — for God’s sake — wear a mask.”

The president also reeled off a list of reasons he said the vaccination campaign is not going faster: the purported lack of a plan by his predecessor, the recent winter storms that shellacked Texas and other states and an initial shortage in supply.

“The story of this vaccination campaign is like the story of everything hard and new America does — some confusion, setbacks at the start, and then if we do the right things, we have the right plan to get things moving,” Biden said. “That’s what we’re seeing right now.”

Biden also stressed that he could not “give you a date” on when life in the United States would return to normalcy, but that “we’ll work as hard as we can to make that day come as soon as possible.”

Before he delivered his remarks in the South Court auditorium of the White House, Biden stood by and watched as a quartet of Americans — a school counselor, a grocery store manager and two firefighter EMTs — got their first round of the Pfizer vaccine, part of a continued public-relations effort to promote getting inoculated from the deadly virus that has killed more than 500,000 people in the United States.

Biden said his administration would undertake a much more aggressive education campaign soon about the importance of being vaccinated and how to get the shots. He warned that in two or three months, the nation could hit a point where it has an ample supply of doses, but too few people who either want them or can access them.

“If there is one message that needs to cut through — vaccines are safe and effective,” Biden said.

He also used the event to promote two of his main pandemic-related priorities in Congress — the confirmation of Xavier Becerra, his pick to become secretary of Health and Human Services, and passage of a $1.9 trillion coronavirus relief package that is slated for a House vote this week.

Later, in a virtual address to governors, Biden pushed them to support the massive rescue plan, citing the state and local relief included in the package. The president said more than 400 mayors had contacted him in support of the package, which includes $350 billion in funding for cities and states.

“The economic toll of this pandemic continues to tear through our country as brutally as the virus itself,” Biden told the governors. “We just have to step up. The economic toll we have to address with the same aggressiveness and seriousness of purpose as we do the virus. And that’s what the American Rescue Plan does.”