Trump said he had been congratulated by leaders around the world.
"It's been an incredible effort," he said.
Trump said that Pfizer announced on Monday that its vaccine was 90 per cent effective.
The White House has given Pfizer nearly US$2 billion for the vaccine and that it would provide doses to Americans "free of charge".
President Donald Trump during an event on Operation Warp Speed in the Rose Garden of the White House. Photo / AP
Pfizer made "an unfortunate misrepresentation", Trump said, when the company said the vaccine development was not part of Operation Warp Speed.
Pfizer did not accept federal funding to help develop or manufacture the vaccine, unlike front-runners Moderna and AstraZeneca, the New York Times reported.
Pfizer has distanced itself from Trump and Operation Warp Speed.
In an interview with the New York Times, Kathrin Jansen, a senior vice president and the head of vaccine research and development at Pfizer, said, "We were never part of the Warp Speed," adding, "we have never taken any money from the U.S. government, or from anyone."
Authorisation for the vaccine would come down "very soon", Trump said.
"It will be approved very very quickly, we hope," he said.
Trump said in April the vaccine would be available for the general public, except in New York state.
"This is a very successful, amazing vaccine," he said.
Trump claimed the US had among the lowest fatality rates for Covid-19 in the world and claimed the US had performed better than "peer countries," without listing any.
Trump also said the drug cocktail which he took when he was a Covid-19 patient would be available to other patients.
"We have some tremendously promising drugs," he said.
Trump claimed there wasn't one person in the US who had requested a ventilator and didn't get one.
The Trump campaign team is still pursuing legal action to contest the results but experts say none of the cases are expected to alter the results.
As it stands, Biden has won the US election with 306 electoral votes - the same number of electoral votes that gave Trump the victory four years ago.
Breaking News: President-elect Joe Biden won Georgia, a major victory for Democrats, and President Trump took North Carolina. The results do not affect the overall election outcome. https://t.co/SSIFp1hDOdpic.twitter.com/tF2KjmZm10
Mr Trump has also been talking about Wisconsin (where Mr Biden leads by 20,000) and Michigan (where he leads by 148,000). There is going to be a recount in Wisconsin, though it would be most unusual for that to shift more than a few hundred votes.
The most fundamental point here hasn't changed – Mr Trump and his lawyers have yet to produce any evidence to back up their claims of widespread fraud. None of the lawsuits they've filed so far would threaten Mr Biden's margin in a single one of the states listed above.
Put aside the fact that many of those lawsuits have been promptly thrown out by judges due to lack of proof. They simply don't involve enough votes to shift the election's outcome anyway.
