The nation's top infectious disease expert, Dr. Anthony Fauci, said that the distribution of COVID-19 vaccines is picking up speed and could be fully on track within a week or so.

"It's just trying to get a massive vaccine program started and getting off on the right foot. The important thing is to see what's happening in the next week, to week and a half," Fauci was quoted on a Bloomberg report.

Surgeon General Jerome Adams said first vaccination program had been superimposed upon a surge of COVID-19 cases. This affected health care resources as well as staff on the holiday season.

Fauci was also the director of the National Institute of Allergy and Infectious Diseases.

The infectious disease expert also said that in the past 72 hours, around 1.5 million vaccine doses have been given, which is about 500,000 per day. Fauci said that they are not where they want to be, adding that they can reach it if they accelerate.

Meanwhile, Operation Warp Speed has so far failed to meet projections for how quickly people will be vaccinated.

Trump earlier claimed in tweets on Sunday morning that case numbers were being exaggerated and deaths were wrongly attributed. Fauci told Trump that he should go to hospitals and intensive care units to better see the situation.

Surgeon general Dr. Jerome Adams also contradicted Trump's false claims that the COVID-19 death toll was far exaggerated.

"I have no reason to doubt those numbers, and I think people need to be very aware that it is not just about the deaths, as we talked about earlier," Adams was quoted on The Guardian report.

Related story: WHO Releases COVID-19 Vaccine Distribution Plan

Four million doses already delivered

The U.S. government has vowed that 20 million Americans would receive a first vaccine dose by Jan. 1. However, two days after the new year has entered, nearly four million doses have only been administered.

Fauci said that there were no excuses for this. Johns Hopkins University data showed that more than 20 million have been infected. Meanwhile, the Covid Tracking Project showed 123,614 people were hospitalized on Saturday.

In addition, Trump administration was reported to be in talks with Moderna to halve the dosage and allow more people to be vaccinated.

Operation Warp Speed adviser Dr. Moncef Slaoui insists that it is not reasonable to alter the vaccine programs, according to a Fox News report.

Slaoui, like Fauci, insists that the vaccine distribution programs are going according to schedule.

The Operation Warp Speed adviser also said that all targets for distribution have been met, with all states receiving their part of the vaccine program.

Slaoui noted that it is an issue with the states deciding what to do with the vaccines. He does not think they are able to identify which long-term care facility or which CVS store should be getting which vaccine or how much vaccine.

He added that it has to be done by people who have the exact knowledge of their population and their movements.

Related story: Government Wants COVID-19 Vaccine Distribution Ready by November