Nicola Sturgeon has written to Boris Johnson calling for urgent four-nation talks to tighten lockdown restrictions further.
The Scottish first minister cited scientific opinion that stronger action was needed to control coronavirus.
Ms Sturgeon also said more financial support was necessary to cushion the impact on businesses.
It comes as the chancellor prepares to unveil plans to minimise job losses as new Covid restrictions come into force.
In July, about 700,000 workers in Scotland, many in the hospitality sector, were still receiving some or all of their income through the scheme.
The Scottish government has already gone further than the Westminster government in introducing restrictions to limit the spread of the virus, by banning different households from meeting inside their homes.
As in other parts of the UK, a 22:00 "curfew" for bars and restaurants will be introduced in Scotland later this week - but at her daily coronavirus briefing on Wednesday, Ms Sturgeon hinted she believed this did not go far enough.
She said if more money had been available to help the hospitality sector it was "likely" she would have come to a "different decision".
In her letter to the prime minister, she said the collective agreement to drive down Covid to the lowest possible level was "particularly welcome".
But she continued: "While all four governments announced new restrictions yesterday, there is clearly a significant strand of scientific opinion to the effect that bringing R back below one and the virus back under control will require measures beyond those which any of us have so far announced.
"In my view, there is considerable force in that opinion."
Ms Sturgeon said experience from earlier this year had shown how essential acting "quickly and decisively" against the virus had been.
"In other words, if we believe further action will be required there is nothing to be gained - and potentially much to be lost, including lives - from delay."
Ms Sturgeon said the four nations should discuss what further actions might be necessary, what support was required for affected sectors and what arrangements could be put in place to ensure that devolved administrations were not constrained when making what they judge to be essential public health decisions.
The Scottish government has repeatedly called for greater borrowing powers as it seeks to alleviate the impact of the pandemic.
In response to Ms Sturgeon's letter, the UK government highlighted the support being given through the Treasury to mitigate the effects of the pandemic.
A spokeswoman said: "The prime minister held a Cobra meeting on Tuesday which was attended by the leaders of the devolved administrations.
"This crisis has shown clearly the value of Scotland being part of a strong United Kingdom, with the UK government providing the bulk of Covid testing in Scotland, the UK's armed forces playing a key role in providing support for Scottish communities, and the UK Treasury playing an absolutely critical role in supporting jobs and business across Scotland.
"We will continue to tackle this pandemic as one United Kingdom."