Nicola Sturgeon has said the way elderly people were discharged from hospital to care homes in the early stages of the pandemic was a mistake.
More than 1,300 elderly people were sent to care homes before a robust testing regime was in place.
Ms Sturgeon said with "hindsight" she agreed with Health Secretary Jeane Freeman's view that this was mistaken.
She has called for a four nations inquiry into the pandemic by the end of the year.
In the early stages of the pandemic, hundreds of elderly people who no longer needed to be in hospital were discharged, in many cases to care homes.
This was at a time when the Scottish government was being advised to create as much spare capacity as possible in hospitals in anticipation of huge case numbers, and before a rigorous testing regime was in place.
Earlier this month, the health secretary said the government failed to properly understand the needs of social care during the pandemic.
She said: "We didn't take the right precautions to make sure that older people leaving hospital going into care homes were as safe as they could be and that was a mistake."
In an interview with BBC Scotland, Ms Sturgeon was asked if she agreed with this analysis.
She said: "Looking back on that now, with the knowledge we have now and with the benefit of hindsight, yes."
She later tweeted, emphasising that decisions were taken based on knowledge that was available at the time, but that it was important to be "candid" about what happened.
What I said is that with the benefit of knowledge we have now (but did not have then), it was a mistake. But too many people in care homes died and we must be candid about that. I hope the other UK govts will join me in committing to a full public inquiry starting later this year https://t.co/QS2oxuK5Do— Nicola Sturgeon (@NicolaSturgeon) April 18, 2021
The first minister said the Scottish government changed the approach when it learned more about how Covid patients without symptoms could spread the virus.
Asked if discharging untested patients from hospitals into care homes had cost lives, she said: "The number of people who died were too many and we got some things wrong and I feel the responsibility of that every single day."
Scottish Labour leader Anas Sarwar said the situation in care homes had been the "biggest crisis" of the pandemic.
He said: "We should never have been sending Covid-positive patients into care homes. That was unforgivable."
Ms Sturgeon told BBC Scotland she wants a judge-led public inquiry into how Covid was handled to begin before the end of this year.
She said her preference was for an inquiry to be established on a UK-wide basis and take account of devolved decision making, but she was prepared to go it alone.
She explained: "I can't force other governments to agree to it, so if we can't get that agreement in good time I will move ahead with a Scottish-only public inquiry".
Other Holyrood parties have suggested distinct Scottish and UK inquiries should be set up and work together.
Mr Sarwar wants a Scottish inquiry running alongside a wider UK investigation, while Scottish Conservative leader Douglas Ross said: "It is right that there are inquiries and I think we'll see them both here in Scotland and across the UK."
The Scottish Liberal Democrat leader Willie Rennie said: "there would be an advantage in Scotland actually starting that process, if the UK isn't prepared to come along at this stage."
The Scottish Greens co-leader Patrick Harvie said: "The Scottish government's response to the pandemic, including its reluctance to diverge from the UK government's approach, must be examined."