Citing numbers suggesting the growth in Philadelphia’s COVID-19 cases may be slowing, city Health Commissioner Thomas Farley pushed back Wednesday on an assertion by the White House’s coronavirus response director that the city could become a virus hot spot.

“I don’t know what numbers she’s looking at,” Farley said in a midday news conference, referring to a television interview hours earlier with Dr. Deborah Birx. “I doubt she’s looking at numbers as updated as we are. So I’m glad that she’s concerned about Philadelphia. We have been hit hard so far, but at the moment, things are better.”

The 505 new cases reported Wednesday is a smaller daily tally than the city has seen in recent days, Farley said. The city now has 4,777 confirmed cases of the coronavirus. The city announced 13 new deaths Wednesday and a total of 78 deaths connected to the coronavirus.

“I’m not saying it’s turning around, I’m not even saying it’s plateauing, but the growth is slowing,” Farley said.

Yet later Wednesday afternoon, Gov. Tom Wolf appeared to embrace Birx’s concerns about Philadelphia, as a way to get more protective gear for medical workers and first responders.

“While it’s not good news that Philadelphia and the southeastern part of the state is seen as a hot spot, it is going to be helpful in getting more resources," Wolf said.

During an appearance on Good Morning America on Wednesday, Birx said the White House Coronavirus Task Force has been looking for trends. "We are concerned about the metro area of Washington and Baltimore, and we’re concerned right now about the Philadelphia area,” she said.

Birx didn’t offer any specifics about Philadelphia, and the White House did not respond to multiple requests for clarification.

Wolf said he learned in a phone call from Vice President Mike Pence that "the federal government is actually bumping Pennsylvania up in terms of priority for getting this scarce personal protective equipment.”

Asked by reporters to reconcile the apparent discrepancy in outlooks, Pennsylvania Health Secretary Rachel Levine said, “I think both are true."

“Stabilizing," Levine said, “means the curve has flattened somewhat. It’s not going up in this exponential way, but [cases] have been increasing.”

In a White House briefing Wednesday night, Pence named Philadelphia as a place of concern and mentioned his conversation with Wolf.

“As we begin to see early trend lines in Philadelphia, I assured him we would continue to flow resources and support to that community,” said Pence.

He also urged the city’s residents to practice social distancing.

Farley said he thought federal authorities may be using models relying on older data for their projections. City officials based their conclusions on the trends in new cases reported each day.

Farley warned that it is far too soon to ease social distancing measures, much less resume normal activities.

“It’s important to say that we can’t assume that slower growth will continue,” he said. “This virus may find new populations, and we may see more rises and falls before we see a sustained fall.”

A model from the University of Washington’s Institute for Health Metrics and Evaluation, said to be a frequent White House resource, anticipated Pennsylvania’s peak demand for hospital resources arriving on Monday. On that day, the model predicted, patients would need 2,180 hospital beds and 418 intensive care beds.

The state should be able to manage that demand, according to the model, which predicts deaths in Pennsylvania to peak Tuesday, though the margin of error is huge.

Michael T. LeVasseur, a professor of epidemiology and biostatistics at Drexel University’s Dornsife School of Public Health, said public health officials and policymakers should be cautious with models.

“All models are wrong; some are useful,” LeVasseur said, quoting the late British statistician George E.P. Box. “All of these models that they are doing are based on giant assumptions. And we still don’t know where we are in Philadelphia. New York has a much better idea, but in Philadelphia, I certainly don’t have an idea where we are.”

Projections depend on so many variables, such as social distancing, that they can be unreliable. “This isn’t the same thing as forecasting a hurricane or a snowstorm," LeVasseur said.

Judging from hospitalization numbers reported by the city and state health departments, the picture doesn’t “look terribly bad, and it looks like it’s improving.”

“So I don’t know where this idea that Philadelphia is going to be a `hot spot’ is coming from,” he said.

State health officials said Wednesday that they were prepared for more COVID-19 patients.

“At this time, our hospital ICU beds have approximately 41% availability, and ventilator availability is over 70%,” said Nate Wardle, a spokesperson for the Pennsylvania Department of Health.

Area hospitals had the luxury of being spared a surge of cases early and have been able to learn from hard-hit New York City, Seattle, and New Orleans, said John J. Lynch III, CEO and president of Main Line Health System.

“For the last three weeks, we’ve had a dedicated group of folks who are spending most of their time on surge planning," he said. "Do we have the beds to put people in? Do we have the ventilators?”

Health-care workers in the region, however, are feeling the strain at their hospitals.

“The numbers are increasing of these patients over the last week or so for sure,” Megan Stobart-Gallagher, an emergency department doctor at Thomas Jefferson University Hospital, said Monday.

Temple University Hospital is treating the largest number of cases locally, according to data shared by the area’s hospitals.

“We’ve been fine up until maybe three days ago, with the increase to the ICU, and that will continue to happen,” said Francine Frezghi, president of the Temple University Hospital Nurses Association, a local of the nurses’ union PASNAP. “You need more ICU nurses than you’ve ever had.”

William C. Pace, an infectious diseases doctor on staff at several area hospitals, including the Jeanes Campus of Temple in Northeast Philadelphia, described similar scenes.

“Every day, we get more and more,” Pace said Sunday. “I was the busiest at Jeanes initially because there was a bunch of people in the Montgomery County area.”

Staff writers Rob Tornoe, Ellie Rushing, and Erin McCarthy contributed to this article.