The pro-independence Scottish National Party Friday secured another term in government with an historic third consecutive victory in Scotland's parliamentary elections but fell short of an outright majority.

In a startling reversal, the Conservative Party scored more seats in the Scottish Parliament than the Labour Party, highlighting Labour's hard times.

The SNP, which advocates independence for Scotland, won 63 seats; the Conservatives took 31 to Labour's 24.

SNP leader Nicola Sturgeon called the party's position "historic" as crowds cheered the results.

"The SNP has won a third consecutive Scottish Parliament election. That has never been done before in the history of the Scottish Parliament. We have tonight made history," she said.

Still, the party will have to make deals with smaller parties or form some sort of coalition to govern effectively.

Just 20 months after losing the independence referendum, in which Scottish voters retained ties to the United Kingdom, the SNP has enjoyed a surge in popularity under Sturgeon's leadership, sparking speculation that another independence referendum may be possible.

In contrast the Labour Party, which had been the official opposition in the Scottish Parliament since 2007, scored its worst-ever result, losing out to the Conservatives for the first time in 60 years.

Labour leader Kezia Dugdale, conceding defeat, admitted the election was always going to be tough for Labour following last year's painful general election setback.

She blamed continuing divisions in Scotland over independence for her party's poor showing.

"I know that for some the constitutional argument remains the most important factor when casting their vote and my determination to try and move the Scottish debate on will have cost me and my party votes tonight," she said.

The Labour Party defeat was seen as a blow to Jeremy Corbyn, who took over the party leadership in the fall.

The Green Party won six seats and the Liberal Democrats won five.