Davidson hails party's record success
Tory leader Ruth Davidson will now lead the official opposition at Holyrood, with Labour finishing in third with 24 seats.
Hailing her party's record success, up from 15 seats in 2011 to 31, Ms Davidson said:
"I hope the message that was resonating was of being a strong opposition, to hold the SNP to account, to saying no to a second independence referendum, to respect the decision that our country made, and to really focus on the things we're paying a government to focus on, on schools, on hospitals, on public services. That's what people want.''
Labour leader Kezia Dugdale has vowed to continue in the job despite the party achieving its worst-ever result at Holyrood, with the loss of 13 seats.
She chose to focus on tax and spending policies during the campaign, claiming Ms Davidson had "poured petrol on the constitutional argument''.
In an email to supporters, she said:
"We fought for what we believe in at this election - for using the power of government to invest in people.
"I hope this result will act as a rallying call for everyone who shares our values to join us. Let's ask those people who we know share our principles to be part of our movement.
"We could have fought an election that was about the arguments of two years ago but we chose to stand up for what we believe in.''
Meanwhile, with the SNP set to form a minority government, both the Greens, with six seats, and the Liberal Democrats, with five seats, could play significant roles in helping Ms Sturgeon pass her legislative programme.
Lib Dem leader Willie Rennie said the SNP must pledge to take another independence referendum within the duration of the parliament "off the table'' to "get over the starting line'' in terms of support from his party.
He said: "They have got to make a clear and unambiguous statement that another referendum must be off the table for the next five years in order to respect the referendum result.
"That's what they need to go just to get over the starting line and I think it's going to be pretty hard for them, but that's what they'll need to do in order to make sure that we can work in partnership.''