The SNP is set to finish well ahead of its rivals, but will likely narrowly miss out on an overall Holyrood majority.
Despite the setback, the First Minister insisted: “We have won more constituency seats than we did in the last election, we have won a higher share of the vote in the constituency ballot than in 2016, and actually we have won more votes and a higher share of the vote than any party in the history of devolution.
“By any standard this is a historic achievement, a quite extraordinary achievement for the SNP – our vote share is up, the vote share of the other main parties is down.”
Tory leader Douglas Ross insisted he would not “shy away” from fighting SNP plans for an independence referendum in the next Parliament.
“I’ll stop talking about independence when the SNP stop talking about independence,” he said.
“The fact that they put it front and centre of their election manifesto meant that I was going to respond to that.
“I’m not going to shy away from the SNP, I’m not going to hide from the crucial debate here in Scotland.”
Scottish Labour leader Anas Sarwar said: “I’m happy compared to where we were ten weeks ago, but am I satisfied in terms of where I want us to get to? Of course not. We are on a journey.”
Meanwhile Lorna Slater, the Scottish Greens co-leader, said she was “excited” at the prospect of a pro-independence majority in Holyrood.
She said: “Certainly we can see that with the Scottish Greens we clearly have a pro-independence majority in the Scottish Parliament.”
But Scottish Liberal Democrats leader Willie Rennie said “now is not the moment” for another Scottish independence referendum after he held his North East Fife seat.
Mr Rennie said: “I hope all the candidates in this election hear the message from the voters that now is not the moment for another referendum.”
Former first minister Alex Salmond has insisted his new Alba Party has put in a “creditable performance” for a party that is six weeks old.