Updated at 9:00 p.m. ET

President Trump and the leading immunologist on the White House coronavirus task force attempted to present a united front Monday, following speculation of a shake-up within the federal pandemic response effort.

Dr. Anthony Fauci — one of the more recognizable faces on the task force — and Trump pushed back on the notion that Fauci was on the outs with the president.

The pair's remarks came in response to weekend comments by both Fauci and Trump that seemed to imply a degree of disagreement between the two on the national coronavirus response.

"Obviously, you could logically say that if you had a process that was ongoing and you started mitigation earlier, you could have saved lives," Fauci said in an interview with CNN on Sunday, seeming to criticize the Trump administration's early efforts to slow the spread of the virus.

Later that evening, Trump retweeted a message from a supporter that read in part: "Time to #FireFauci."

Fauci called his Sunday remarks "a poor choice of words," and Trump said he'd had no intention of removing the doctor from his task force. The White House had put out a statement earlier Monday tamping down such speculation.

Monday's coronavirus task force news conference followed an Easter weekend during which the U.S. death toll from COVID-19 increased to the highest in the world.

In the at-times contentious briefing, Trump defended his handling of the pandemic, including showing reporters a campaign-style video of flattering media clips from throughout the crisis.

As the pandemic continues to ravage the globe, Trump says he plans to unveil a council dedicated to "reopening" the country soon. Members of the committee are expected to be announced this week.

Trump declined to specify exactly when he expected to see restrictions eased on the American public but offered that he expected full cooperation from states, following guidelines from his task force. That's as several governors have banded together to coordinate easing their restrictions.

"The president of the United States has the authority to do what the president has the authority to do, which is very powerful," Trump said. "The president of the United States calls the shots."

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Experts have recently projected a more optimistic outlook on the coronavirus' ultimate impact, lowering the predicted number of U.S. lives lost to 60,000 people, from original projections of 100,000 to 200,000. But the country is still bracing for severe social and economic fallout from the spread of the virus.

Trump last week said he will surround himself with the "greatest minds" to advise him on the best way to approach restarting the country's halted economy.

"We're going to make a decision, and hopefully it's going to be the right decision," he said.

The first wave of the administration's economic relief effort — cash payments of up to $1,200 for adults — began on Friday, Treasury Secretary Steve Mnuchin said at the briefing.

Some 80 million Americans are expected to get their direct deposit by Wednesday.

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