Doses will pick up “significantly” this week after a dip in supply over the last month, Ms Sturgeon told the Covid-19 daily briefing on Monday.
“We are expecting, taking first and second doses together, there will be around 400,000 vaccinations over the course of this week and this represents a significant increase on the level of vaccination we’ve seen over the past couple of weeks,” she said.
“Supplies permitting, that increase is likely to continue into April, that means by the middle of April we are still on track to have offered a first dose of the vaccine to everybody over the age of 50, all unpaid carers and all adults who have particular underlying health conditions.”
The highest weekly total of first and second doses so far given in Scotland was in the second week of February, when just over 392,000 doses were delivered.
The Scottish Government had originally intended to hit the 400,000 a week target by the end of February, but the goal was delayed by a drop in vaccine supply.
Some 1,908,991 people have now received a first dose, and 161,945 received their second dose.
There are also 53 per cent of 60 to 64-year-olds with a first dose, 41 per cent of 55 to 59-year-olds and 33 per cent of 50 to 54-year-olds.
Some 97 per cent of 65 to 69 year olds have had a first dose.
The Scottish Government is investigating a delay to vaccination appointment letters sent out to patients in NHS Lothian last week, Chief Medical Officer Dr Gregor Smith said.
NHS Lothian confirmed the delay on Friday, and said it hoped the problem would be resolved over the weekend.
A spokesperson said the issue was not caused by Royal Mail.
"We’re aware there was a delay in some letters being issued to patients in NHS Lothian towards the end of last week,” said Dr Smith on Monday.
"The letters are issued between NHS Lothian who provide information, and National Services Scotland, who are one of our national supporting boards.
"In this instance there appears to have been some delay in some of those letters reaching patients.
"We’re currently investigating why those delays took place, with NHS Lothian and with NSS, and we may be able to say a little bit more about that in the future.”
Dr Smith said the delay was an isolated incident for people in the Lothian area.
"I’m not aware of any wider issues that there are across Scotland in relation to that,” he said.
NHS Lothian said in a statement on Friday: "Appointment letters are being distributed by a central system to patients across Scotland.
"We understand there has been a delay in sending out some appointment letters this week (March 12).
"This should be resolved very quickly and the letters are expected to arrive by this weekend. However, if you are over 60 and have not received an appointment letter by Monday (March 15), please call the national helpline on 0800 030 8013.”