SNP leader John Swinney has ruled out any negotiations with Reform UK as his party seeks to return to government.
While the SNP comfortably won a fifth successive Holyrood election, the party is seven seats short of a majority - meaning it will have to rely on help from other parties to pass laws.
Labour and Reform UK came joint second with 17 seats each, followed by the Greens on 15, the Conservatives on 12 and the Liberal Democrats on 10.
Reform's leader in Scotland, Malcolm Offord, accused Swinney of being "arrogant, petty and deeply undemocratic".
Swinney told a news conference in Edinburgh that the SNP was by a "country mile" the leading party and would form the next government.
He said the leaders of all other Holyrood parties would be invited individually to talks from next week - except for Reform.
Swinney pointed to successful budget negotiations with the Greens and Lib Dems earlier this year, and said the party had worked constructively with the Tories and Labour on other issues.
However, the SNP leader said Reform's leader in Scotland, Malcolm Offord, would not be invited for talks.
The SNP leader said that election results in England, where Reform racked up more than 1,400 councillors, and in Wales, where it is the second largest party behind Plaid Cymru in the Senedd, showed the urgent need for independence.
He warned that Nigel Farage was "galloping" towards Downing Street, which he said would be "catastrophic".
Swinney told the news conference: "It is vital that we unite in Scotland to ensure our parliament is fully Farage-proofed.
"That means having the power before 2029 to decide our own constitutional future without Farage being able to block us."
He added that after Plaid Cymru's success, Scotland, Wales and Northern Ireland all had first ministers "committed to fundamental constitutional change".
Swinney said he had hoped to win an SNP majority to break the constitutional "logjam" and secure a second independence referendum.
Such a vote would need to be signed off by the UK government, as it was when the first Scottish independence poll was held in 2014. However, Westminster has repeatedly refused to countenance the idea.
Swinney insisted Holyrood had a mandate for such a vote, pointing out that between the SNP and Greens there were more pro-independence MSPs at Holyrood than ever before.
The SNP leader also insisted that his ambition of holding a referendum in 2028 was realistic.
"There has now been a pro-independence majority for four elections in a row but this mandate has been ignored by both Labour and Tory prime ministers year after year," Swinney said.
Although the SNP comfortably won the election, their constituency vote share was down by almost 10% compared to the last Holyrood election in 2021, while the regional vote share fell by more than 13%.
The combined pro-independence SNP and Green vote share was just over 40% across both constituencies and regions.
Offord described independence as a "dead duck", adding: "It's not going to happen."
He accused Swinney of "exactly the kind of out-of-touch establishment politics people are sick of".
Offord said: "The SNP can lock the doors of St Andrew's House if they like but they cannot shut down the growing demand for real change in Scotland."
Scottish Conservative leader Russell Findlay claimed Swinney was "shamelessly attempting to move the goalposts" on independence.
He said: "He is brazenly peddling a massive lie by claiming that he has the support and the mandate for another divisive referendum."
Findlay told BBC Scotland News that his party was the only "strong, credible voice of opposition" at the Scottish Parliament, despite its worst ever performance in a Holyrood election.
Scottish Greens co-leader Ross Greer said there was no need for Reform to be part of cross-party talks in the new Scottish Parliament.
Greer said his party would continue to "work constructively" with a new SNP government, and identified measures to ease the cost of living as his priority.
Scottish Lib Dem leader Alex Cole-Hamilton said his party had deprived the SNP of a majority, meaning the question of another independence referendum should be "put in the deep freeze for at least the next five years".
He said he hoped the parliament of minorities would work constructively to find consensus.
Unlike other parties, Scottish Labour did not hold a media event on Saturday.
