Public Health Minister Anutin Charnvirakul admits he received a letter from the AstraZeneca company saying it has the capacity to supply Thailand with just three million doses of its vaccine a month.
However, Mr Anutin insisted he wrote back to say the country needed at least 10 million doses a month to combat surging daily infections.
The company's letter was dated June 25 and Mr Anutin's reply was made five days later.
In an interview with Isranews Agency, which obtained the leaked letter, Mr Anutin said he argued the country needed a much larger quantity. He advocated for at least 10 million doses a month for the national vaccination campaign.
Mr Anutin said Prime Minister Prayut Chan-o-cha backed his stance.
The minister said the government hoped AstraZeneca will be able to deliver the vaccine to meet the government's target.
The correspondence came as vaccine supplies are reportedly running short, forcing several non-hospital vaccination points in Bangkok to suspend operations.
On Thursday, AstraZeneca asked Thailand to extend the timeline for delivery of 61 million doses of its Covid-19 vaccine until May next year, Deputy Public Health Minister Sathit Pitutecha said. The move was feared to strike a further blow to the country's vaccine roll-out.
In its letter, AstraZeneca referred to an agreement reached in September last year that it would supply the Public Health Ministry with one-third of the vaccines it can produce, or three million doses per month.
It intends to export the remaining two-thirds, spurring talks about the government placing curbs on vaccine exports to ensure local supplies are met first.
In his reply, the minister said the government expected the company to roll out more than one-third for Thailand.
On Saturday, the minister said the Department of Disease Control (DoDC) has been in talks with its contractual partner, AstraZeneca (Thailand), to increase vaccine supplies and deliver them as fast as possible.
The talks are conducted through a special panel comprised of DoDC director-general Opas Karnkawinpong, National Vaccine Institute director Nakhon Premsri and legal experts.
"The government will get hold of the vaccine and administer it to every Thai citizen until the virus is wiped out or becomes a common disease," Mr Anutin said.