President Trump on Tuesday said the distribution of the Pfizer and Moderna coronavirus vaccines is going "very smoothly," calling the efforts of his administration to complete vaccines against COVID-19 a "great miracle."

"Distribution of both vaccines is going very smoothly," the president tweeted. "Amazing how many people are being vaccinated, record numbers."

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"Our Country, and indeed the World, will soon see the great miracle of what the Trump administration has accomplished," Trump continued. "They said it couldn’t be done!!!"

The president’s comments come as the federal government is rolling out nearly 8 million doses of COVID-19 vaccines this week – between products from Pfizer and Moderna.

An independent advisory panel for the Centers for Disease Control and Prevention over the weekend voted to recommend the next wave of vaccines go to front-line essential workers and people over the age of 75.

This group would comprise about 51 million people, and stand in line behind about 3 million nursing home residents and 21 million front-line medical workers who held first priority for Pfizer’s initial wave of vaccines rolled out last week. However, the panel, Advisory Committee on Immunization Practices (ACIP), noted there will likely be overlap between phases.

As for aid to nations around the world, the president earlier this month signed an executive order that ensures Americans have access to the coronavirus vaccine before the U.S. government begins aiding nations around the world.

Senior administration officials told Fox News earlier this month that the president will re-emphasize to the American people that the "priority has been an America First approach."

"We work with the world," Trump said earlier this month upon signing the order. "We’re working with the world."

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The president said the order ensures "the U.S. government prioritizes the getting out of the vaccine to American citizens before sending it to other nations."

A senior administration official told Fox News last week that the "priority" is to distribute to Americans, and predicted that international assistance could come "late spring, early summer," and after they "achieve vaccinating those [in the U.S.] who have a desire to be vaccinated."

As of Monday, the U.S. has distributed over 2.8 million doses of COVID-19 vaccines, and some 556,208 people have received the first of their two-dose vaccinations, according to the CDC.

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The U.S. topped 17 million infections just last Thursday, Dec. 17. As of Tuesday morning, the U.S. has already reached more than 18 million reported cases, according to data from Johns Hopkins University, and at least 319,466 people had died due to the disease.

Fox News' Kayla Rivas contributed to this report.