Boris Johnson referred to the Treasury as the "pro-death squad" during a meeting to discuss lifting lockdown restrictions in January 2021, the Covid Inquiry has heard.
The phrase appears in a diary entry written by then chief scientific adviser Sir Patrick Vallance.
Giving evidence on Monday, senior civil servant Stuart Glassborow said he did not remember hearing the term.
Mr Johnson is expected to appear before the inquiry next month.
Strict lockdown restrictions were re-imposed in late 2020 as the UK tackled a spike in infections and the emergence of a new variant of the virus.
Dermot Keating, counsel to the inquiry, read from the private diaries of Sir Patrick Vallance, extracts of which have been released before he gives evidence later this month.
By the end of January 2021, officials were debating how quickly to ease lockdown rules and move regions of England out of a series of staggered tiers - each with lighter restrictions.
"There is an entry... at a meeting on 25 January 2021, the PM is recorded saying he wants Tier 3 [by] 1 March, Tier 2 [by] 1 April, Tier 1 [by] 1 May and nothing by September," said Mr Keating.
"And he ends it by saying the team must bring in the pro-death squad from [HM Treasury]".
Sir Patrick's diaries have been described as a "brain dump" by his legal counsel and a way to process the events of the day and protect his mental health.
Asked about Sir Patrick's description of the meeting, Mr Glassborow - the PM's deputy principal private secretary at the time - said: "I would not dispute what he's recorded, but I don't recall the phrase at all."
Earlier in the day, the inquiry was also shown a briefing paper sent by Treasury officials to then Chancellor Rishi Sunak in September 2020 in which he was advised to "push back strongly on the circuit-breaker proposal".
Around that time, the government's Sage group of scientific advisers was recommending tightening restrictions including the "consideration" of a short circuit-breaker lockdown.
The note - written ahead of a key meeting of officials to discuss the spread of the virus - said further measures to strengthen the rules were "likely to be catastrophic" for the economy.
Mr Sunak has previously said he had opposed stricter measures at the time but that the final decision lay with the prime minister.
The inquiry was later shown a series of WhatsApp messages sent in September and October 2020 between then Downing Street director of communications Lee Cain and Ben Warner - a data scientist hired by Dominic Cummings after working on the 2016 Vote Leave campaign.
"Why are we not acting in London and urban areas now? Same errors as March," Mr Cain wrote to Mr Warner on 12 October.
Mr Warner replied: "Agreed. Feel like we are where we knew we would be three/four weeks ago."
On 30 October, Mr Warner sent another message: "I feel like I have accidentally invented a time machine".
Cain replied: "Oh mate. I can't take this insanity."
Asked about the exchange, Mr Warner said he believed infections would continue to rise until more stringent restrictions were put in place and that other measures, such as the test and trace system, were not able to control the virus.
"We [were] seeing that infections keep rising until you do something," he said.
Mr Warner also told the inquiry he was "continually concerned" by the lack of scientific understanding across government departments outside of of the Sage group.
"Throughout the pandemic, I thought that there was a lack of scientific capability within the different teams and groups that I was working with," he added.