US officials on Sunday rejected Donald Trump's claim that the national Covid-19 death toll of more than 350,000 has been exaggerated, but defended the stumbling campaign to vaccinate millions of Americans.

Some 4.2 million people in the US have received initial doses of the two-dose vaccines from Pfizer-BioNTech or Moderna -- far below official predictions of 20 million by the new year.

The president blamed local authorities for the delays, tweeting that "the vaccines are being delivered to the states by the Federal Government far faster than they can be administered!"

He also claimed that the number of cases and deaths was "far exaggerated" because of a "ridiculous method of determination," accusing the Centers for Disease Control (CDC) of a policy of "When in doubt, call it Covid."

In response, top US scientist Anthony Fauci said on ABC that "those are real numbers, real people and real deaths."

Surgeon General Jerome Adams, who was nominated by Trump, told CNN that he saw no reason to question the numbers from the federal CDC.

More than 13 million vaccine doses have been distributed nationwide, but efforts to vaccinate health workers and vulnerable people have been hampered by logistical problems and overstretched hospitals and clinics.

"There have been a couple of glitches, that's understandable," Fauci said, adding it was a challenge "trying to get a massive vaccine program started and getting off on the right foot."

Part of the problem, Adams said, was that "a lot of the local capacity to be able to vaccinate was being used for testing and responding to surges."

Fauci said he saw "some little glimmer of hope" in the fact that 500,000 people are now being inoculated a day, a far better number than when the program started last month, and "I think we can get there if we really accelerate, get some momentum going."

Adams said he, too, expects vaccinations to "rapidly ramp up in the new year."

- 'We need to improve' -

Troubling reports have emerged of vaccines going bad due to poor organization, lack of healthcare professionals to administer them or, in one isolated case, sabotage.

Some people have also waited in line for hours only to be turned away.

In Tennessee, elder citizens, some with walkers, were reported standing along a busy highway while waiting for their vaccinations.

Moncef Slaoui, the chief advisor to Operation Warp Speed, the military-led US vaccine effort, told CBS there was an "assumption" that states had plans in place to administer the vaccine.

"We need to improve," he said. "We will do the best we can, as we have done over the last eight months, to make (certain) these vaccines indeed make it into the arms of people."

Another alternative is being explored for the Moderna vaccine, he said: administer half-doses, twice. "We know it induces identical immune response," he explained, saying officials are in discussions with Moderna and the Food and Drug Administration (FDA) about the possibility.

The hardest-hit country in the world by the pandemic, the US has recorded 20.6 million cases overall and 351,452 deaths as of 8:30 pm Sunday (0130 GMT Monday).

Numbers of cases and deaths are expected to soar further after the holidays.