The First Minister said there is "no time to waste" and it would be "unconscionable" for the Treasury not to use its borrowing powers to provide more cash.
Ms Sturgeon previously wrote to Boris Johnson with an urgent plea to bring back furlough in the wake of the alarming spread of Omicron.
The pair have now held talks to discuss the ongoing response to the variant.
A Downing Street spokeswoman said: “The Prime Minister confirmed the UK Government will be convening a Cobra [emergency] meeting over the weekend with counterparts from the devolved administrations to continue discussions.”
A spokesman for the First Minister called the talks “constructive – though at this stage inconclusive”.
Earlier this week, Ms Sturgeon announced an extra £100 million of funding for businesses.
She has now confirmed £66m of this will go to the hospitality sector, £8m to the food and drink supply chain, £20m to the culture sector, £3m to the wedding sector, and £3m to the "worst affected parts of tourism".
She said this support was "significant", but conceded it would not "fully compensate these sectors for the impact they're suffering right now".
Speaking at a coronavirus briefing, Ms Sturgeon said: "The UK Government has to get its finger out. It has to step up and it has to provide this support."
She said Chancellor Rishi Sunak should have "no other job today than to get in place the financial support mechanisms that help hospitality, culture and the wider economy as we go through this next difficult phase".
In a letter to the Prime Minister on Thursday, Ms Sturgeon said the return of restrictions on "higher risk settings" may now be “unavoidable".
The Treasury has said it is providing Scotland with £220m of additional funding, but Ms Sturgeon insists this is not new money.
Creative Scotland welcomed the Scottish Government cash.
But Colin Wilkinson, managing director of the Scottish Licensed Trade Association, raised concerns some of the £66m for hospitality could be “misdirected” to cafes, takeaways and even multinational fast food outlets, which are “far less in need of support”.