The SNP leader was speaking as she met her fellow 62 MSPs following Thursday’s Holyrood election.
While the nationalists won the election, Ms Sturgeon and her party will have to come to terms with losing their overall majority and with a new opposition, led by Tory Ruth Davidson after she relegated Labour to third place in the Scottish Parliament.
The SNP members elected fell two short of a majority and Ms Sturgeon announced on Friday she will lead a minority administration at Holyrood - ruling out speculation over possible coalition.
Her potential allies have warned she will not get an easy ride implementing the SNP’s programme for government.
Lacking an overall majority, she will need the support of other parties to be re-elected as First Minister and to pass legislation.
Speaking at a party event at the Kelpies statues in Falkirk, Ms Sturgeon said when parliament reconvenes she would ask to be re-elected as First Minister.
She she said: “The government I lead will be open and it will be inclusive.
“It will be a government that reaches out and strives to find and to build on common ground.
“And I believe there is common ground to be found on education, on the economy, on the environment and I am sure on many other issues.
“That is my commitment, to work above party boundaries in the best interest of our country.”
Ms Sturgeon added: “I would also say this to the opposition parities, the SNP won the election.
“We won the election overwhelmingly, so yes we will compromise where that is in the best interests of our country but we have a clear and unequivocal mandate to implement the manifesto that we fought and won this election on.
“And we have the right to assert the values and positions set out in that manifesto.
“So the work to build an even better and stronger Scotland begins here today.”
Both the Scottish Greens - with six seats, and the Liberal Democrats - with five seats, could be key in helping the SNP ensure its laws pass through parliament.
The Greens propped up the last nationalist minority administration in 2007 and co-convener Patrick Harvie said it now intends to push the SNP “beyond its comfort zone”.
The Lib Dems, veteran coalition builders with a reputation for compromise, talked tough with leader Willie Rennie insisting the “arrogant” SNP now needs “a change of attitude”.
The Scottish Conservatives won a record 31 seats, up from 15 in 2011, and are now Holyrood’s second biggest party.
The Tories won a number of concessions from Alex Salmond’s minority administration and leader Ruth Davidson has pledged to “work constructively where required” but “provide challenge where they do not listen”.
Both the Tories and the Lib Dems insisted the one thing they will not compromise over is another independence referendum, with Ms Davidson saying the SNP had “no mandate, no majority, no cause” and Mr Rennie insisting it must be “off the table”.
Kezia Dugdale has pledged to continue as Scottish Labour leader following its worst ever result of 24 seats, down 13 from 2011.
She said the result was “heartbreaking” but vowed to “keep fighting for Labour values”.