The comments undermined the director of the Centres for Disease Control and Prevention’s (CDC) projections for a longer time frame.
Mr Trump also disagreed with Dr Robert Redfield about the effectiveness of protective masks — which the president recommends but almost never wears — and said he would telephone Dr Redfield to tell him so.
Earlier in the day, the CDC sent all 50 states a “playbook” for distribution of a vaccine to all Americans free of cost when one is proven safe and effective.
Dr Redfield told a congressional hearing that health care workers, first responders and others at high risk would get the vaccine first, perhaps in January or even late this year, but it was unlikely to be available more broadly before late spring or summer.
After Mr Trump’s comments, CDC officials said that the director had thought he was answering a question about when vaccination of all Americans might be completed.
Dr Redfield, masked at times in a Senate hearing room, also spoke emphatically of the importance of everyone wearing protective masks to stop the pandemic, which has killed nearly 200,000 Americans.
He floated the possibility that a vaccine might be 70% effective in inducing immunity, and said, “I might even go so far as to say that this face mask is more guaranteed to protect me against Covid than when I take a Covid vaccine.”
The president would have none of that from the CDC director.
“Vaccine is much more effective than the mask,” he declared.
As for vaccinating Americans, Mr Trump said on Wednesday: “We think we can start sometime in October.”
One of his recently added advisers, Dr Scott Atlas, said as many as 700 million doses could be available by the end of March.
The president made the prediction even though the vaccine is still being tested in human subjects, and some health experts have said they believe a safe and highly effective vaccine is several months way, if not much longer.
We’re ready to move, and I think it will be full distribution
CDC sent a planning document on Wednesday to US states, territories and some big cities.
Adding to logistical complications, vaccines likely will have to be given in two doses spaced weeks apart and will have to be refrigerated.
Dr Redfield said states are not ready to deal with the demand for such a distribution and some $6 billion (£4.62 billion) in new funding would be needed to get the nation prepared.
Unswayed, Mr Trump said: “We’re ready to move, and I think it will be full distribution.”
The vaccine would not be broadly available until the spring or summer 2021, Dr Redfield estimated.
He also rejected questions about whether the CDC’s timeline for states to be ready for a vaccine by November 1 was politically motivated.
“The worst thing that could happen is if we have a vaccine delivered and we’re still not ready to distribute,” Dr Redfield told Senate lawmakers.
“There was absolutely no political thinking about it.”
Democratic presidential nominee Joe Biden said while campaigning that he trusts what scientists say about a potential vaccine — but not Mr Trump.
Mr Biden has said he would take a vaccine “tomorrow” if it were available but he would want to “see what the scientists said” first.
As for the planned vaccine campaign, Dr Redfield said his agency will be working with state health officials to implement the preparations in coming days.