The United States, which has reported the world's worst overall Covid-19 death toll, has "no doubt" been undercounting fatal cases, top pandemic advisor Anthony Fauci said Sunday.

The country has officially lost over 581,000 people to the disease caused by the SARS-CoV-2 coronavirus -- but a University of Washington study released Thursday estimated deaths at more than 900,000.

"That's a bit more than I would have thought the undercounting was," Fauci told NBC's "Meet The Press." "But I think there's no doubt... that we are and have been undercounting." The United States has reported over 32.6 million cases since the virus was first identified at the end of 2019 in China.

America was battered by a spike in cases and deaths after the end-of-year holidays, but since January new infections have come down as vaccination rates have jumped.

"We are turning the corner. We have 58 percent of adult Americans with at least one shot, over 110 million Americans fully vaccinated," White House COVID-19 coordinator Jeffrey Zients told CNN's State of the Union.

President Joe Biden wants 70 percent of adults in the US to have received at least one shot of the COVID-19 vaccine by the July 4 Independence Day holiday.

But the rate peaked around April 10 and has been declining since then, with vaccine hold-outs slowing the race to population immunity.

Federal, state and local officials are partnering with pharmacies, restaurants, breweries, supermarkets and sports teams to come up with incentives to get people to get their shots.

In New Jersey, Governor Phil Murphy launched a "Shot and a Beer" program to encourage vaccination, while in West Virginia Governor Jim Justice announced that the state will offer $100 savings bonds to residents aged 16 to 35 who get inoculated.