Boris Johnson's government has offered to help Scotland with its coronavirus vaccine rollout.
But the first minister launched a staunch defence of her government's vaccine rollout during an appearance in front of MSPs to update them on lockdown measures.
Scotland Secretary Alister Jack has written to Ms Sturgeon, restating the UK government's "full support in rolling out the vaccination programme and fighting the pandemic across the whole country".
"I'm sure you would agree with me that it is in everyone's interests that progress in vaccinating the people of Scotland matches the best efforts of the rest of the UK," he wrote.
"With that in mind, we stand ready to offer any support or assistance we can give you to accelerate your rollout programme."
Mr Jack implored Edinburgh to accept the offer of assistance, saying: "I strongly believe that to put the nightmare of COVID-19 behind us as quickly as possible, we must collaborate as closely as possible."
A total of 610,778 people in Scotland have received the first dose of a vaccine, out of an adult population of 4.4 million, which is 13.8%.
By contrast, 18.9% of adults in England have been given a jab, compared with 17.4% in Wales and 16.1% in Northern Ireland.
Facing MSPs in the Scottish parliament on Tuesday, Ms Sturgeon acknowledged that her government wanted to "accelerate the overall progress" of the vaccination campaign.
She said just under 35,000 first doses were administered on Monday, a record daily total and 55% more than the number given on the same day last week.
But Ruth Davidson, Holyrood leader of the Scottish Conservatives, noted that on Sunday, "Scotland saw the lowest number of jabs administered since the start of the mass rollout over a month ago".
She added: "At the moment, all the evidence shows the Scottish government's rollout is slow, stuttering and lagging way behind the rest of the UK."
Ms Davidson said the proportion of 75-79-year-olds vaccinated in Scotland - 21% - was "just a quarter of the proportion vaccinated south of the border".
Responding to the criticism, the first minister said the number of jabs would increase "as we make more use of mass vaccination centres for the younger age groups", with two new mass vaccination centres now open in Edinburgh and Aberdeen.
The first minister said 98% of older people in care homes and 88% of staff had received their first vaccine dose.
"That really matters in terms of reducing the burden of illness and deaths," Ms Sturgeon said.
She added that almost 90% of those over 80 had been inoculated, while the number of over-70s will "grow day by day in this week".
Everyone over the age of 70, as well as adults classed as clinically extremely vulnerable, will get an appointment letter by the end of the week, Ms Sturgeon said.
And she told MSPs that Scotland was on course to meet its target of vaccinating everyone in these groups by the middle of this month.
"I'm not standing here denying we want to accelerate the overall progress," the first minister said.
"But nor will I apologise for having deliberately focused on maximising uptake in the most clinically vulnerable groups."