The First Minister of Scotland pointed to scientific opinion that bringing the virus back under control will require measures beyond those announced so far in a letter to Boris Johnson.
She also highlighted that devolved administrations’ ability to take action is curtailed by a lack of financial levers to deliver economic support.
Ms Sturgeon said “The collective agreement yesterday of the four nations to drive Covid transmission to the lowest possible level and keep it there was particularly welcome.
“However, I am sure you will agree that we must all now act in a manner that can achieve that objective."
The prime minister announced a raft of new measures yesterday aimed at combating the increasing spread of the virus including rules around closing pubs and restaurants at 10pm.
Scotland went further and also limited the ability for different households to mix in other people's homes - a key driver in the increase in infections.
Ms Sturgeron said: “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 1 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.
“It is also the case – and we know this from our experience earlier this year – that acting quickly and decisively against the virus is essential.
“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.
“Therefore, I am writing to request further four nations discussions on three inter-related questions.”