Johnson & Johnson is projected to ship 11 million COVID-19 vaccine doses next week, the White House COVID-19 task force said Friday, which would ensure the company keeps its commitment of delivering 20 million vaccines before the end of March.

Jeffrey Zients, the White House coronavirus coordinator, said during a briefing that Moderna and Pfizer, the manufacturers of the two other authorized vaccines, also appear on track to meet their first quarter targets. He estimated that half of the states would open eligibility to all adults by mid-April.

“We are expecting a significant number of doses, and we’ve talked to the governors and our federal partners,” he said. 

Zients reiterated there should be enough supply for every U.S. adult by the end of May.

The United States has been vaccinating 2.5 million adults per day over the last two weeks, and Zients said that number will likely increase as more vaccine sites open, the supply of vaccines increases and eligibility levels broaden.

At the same time, Centers for Disease Control and Prevention Director Rochelle Walensky cautioned that the most recent seven-day average of 57,000 cases per day is a 7 percent increase from the prior seven days. She also pointed to a slight increase in the seven-day hospitalization rate to 4,700. Deaths continue to hover at about 1,000 per day.

“I remain deeply concerned about this trajectory. We have seen cases and hospital admissions move from historic declines to stagnation to increases,” she said. “We know from prior surges that if we don’t control things now, there is a real potential of the epidemic curve to surge again.”

Former CDC Director Robert Redfield, who served during the Trump administration, told CNN on Friday that he believed COVID-19 likely originated from a Wuhan lab — contrary to the view of the World Health Organization.

Anthony Fauci, director of the National Institute for Allergy and Infectious Diseases, said Redfield was sharing an “opinion of a possibility” but it was more likely the virus was circulating in China for a month before it was clinically recognized.

“There are other alternatives, others that most people hold,” said Fauci. “It was likely below the radar screen, spreading in the community.”

Walensky added U.S. officials are looking forward to an upcoming report from WHO on the origins of the virus. 

“I don’t have any indication for or against either of the hypotheses that Dr. Fauci just outlined,” she said.

The task force also announced that as of Friday, 71 percent of adults 61 and older have received the vaccine, and one-third of all adults have received at least one dose.