The allegation against the prime minister is made in the diary of ex-chief scientific adviser Patrick Vallance.
Vallance made private notes every evening during the pandemic and these have been handed to the official inquiry.
In one entry dated October 25, 2020, Vallance recalls a meeting as arguments raged inside government over whether to impose second lockdown in England.
According to Vallance, Dominic Cummings told Boris Johnson in the meeting: “Rishi says just let people die and that’s okay.”
Vallance does not claim to have himself heard Sunak - who was then chancellor - make that comment.
Downing Street said it would not comment on the accusation. “The prime minister is due to give evidence before the inquiry at the time of their choosing. That’s when he’ll set out his position,” No. 10 said.
In his evidence on Monday, Vallance also said Sunak’s Eat Out To Help Out scheme “obviously” increased transmission of the virus.
The programme, which began in August 2020, cut the cost of food in order to encourage people to visit restaurants and other hospitality venues.
Asked if it had increased the number of deaths from Covid, Vallance said: “It is highly likely to have done so.”
He said: “I think it would have been very obvious to anyone that this inevitably would cause an increase in transmission risk, and I think that would have been known by ministers.”
Vallance said he had not been informed about the scheme before it was announced to the public.
The inquiry was shown a section of Sunak’s written evidence to the inquiry in which he denied government scientists warned against the programme.
“I do not. recall any concerns about the scheme being expressed during ministerial discussions, including those attended bye the CMO [chief medical officer Chris Whitty] and the CSA [chief scientific adviser Vallance]