The results from Thursday's vote have put the issue firmly back on the table and set the stage for a clash with London.
In her victory speech, Scottish First Minister Nicola Sturgeon said her Scottish National Party (SNP) -- which wants to break away from the United Kingdom -- had delivered a "historic and extraordinary" win after finishing with 64 seats in the Scottish parliament, one short of a majority.
Combined with the eight seats won by Scottish Greens, pro-independence parties now control 72 of the parliament's 129 seats. The Conservative party won 31 seats, Labour won 22, and the Liberal Democrats four seats.
Sturgeon said that although her priority was to "lead Scotland through the pandemic and to keep people safe," her party still intends to ask for a second referendum on whether to end the nation's 300-year-old union with England.
Sturgeon also warned that "any Westminster politician" who tries to stand in the way of a referendum is not "picking a fight with the SNP, you're picking a fight with the democratic wishes of the Scottish people."
The comments are likely directed at UK Prime Minister Boris Johnson, whose permission is needed to hold a referendum in Scotland. He has so far refused a second vote, saying a 2014 referendum -- in which Scots voted to remain in the United Kingdom -- was a once-in-a-generation event.
"I think a referendum in the current context is irresponsible and reckless," Johnson told the Daily Telegraph on Friday.
One of Johnson's senior Cabinet ministers on Sunday repeatedly avoided answering the questions of how the government would handle a second independence referendum.
Asked on Sky News if the government would go to the Supreme Court if the Scottish parliament passed a bill to hold a referendum, Cabinet Office minister Michael Gove said "we're not going to go there."
Johnson has invited Sturgeon to join a UK-wide Covid recovery summit and, in a letter, said the United Kingdom was "best served when we work together."
"We will all have our own perspectives and ideas -- and we will not always agree -- but I am confident that by learning from each other we will be able to build back better, in the interests of the people we serve," Johnson wrote.
The prospect of a second independence referendum has been on the cards ever since the 2016 Brexit referendum, when 62% in Scotland voted to remain in the European Union.
Speaking on the BBC's "The Andrew Marr Show" on Sunday, Sturgeon again insisted that voters' support for her party -- which claimed a fourth consecutive win -- gave her a clear mandate to pursue a referendum.
"In this election they have voted overwhelmingly for the SNP and we stood on a manifesto commitment to firstly... continue to steer the country through the Covid pandemic, but after the crisis to give the people of Scotland the opportunity to choose our own future in a referendum," she said.
"The fact that we are sitting here having a debate about whether or not that outcome is going to be respected says a lot about the lack of respect for Scottish democracy that this UK Government has demonstrated over quite some time now."