The Liberal Democrats have turned down the prospect of a coalition with the Scottish National Party to form the next government of Scotland.
Mr Stephen says an independence referendum is the key issue
Scottish Lib Dem leader Nicol Stephen said the fundamental stumbling block was the Nationalists' demand for a referendum on independence.
SNP deputy leader Nicola Sturgeon urged the Lib Dems to sit at the negotiating table in the interests of Scotland.
She insisted there was no alternative to Alex Salmond as first minister.
Mr Stephen predicted there would now be an SNP minority government at Holyrood following Thursday's election.
Earlier, the Lib Dems ruled out a coalition deal with Labour.
The 47 seats won by the SNP made them the largest party in the 129-member Scottish Parliament, but this falls short of a majority, for which 65 seats are needed.
Labour won 46 seats, the Conservatives 17 and the Lib Dems 16, with the Greens on two and one independent.
More than 100,000 ballots were counted as spoiled in the election and in one seat - Cunninghame North - former Labour minister Allan Wilson is considering a legal challenge after losing by 48 votes.
A lawyer is also preparing to contest the outcome of the Glasgow region.
Mr Stephen said he had held talks with the SNP leader Alex Salmond but these had failed to resolve their differences over the referendum.
"I made it clear to him that unless and until the SNP removes the fundamental barrier of a referendum on independence during the next four years, there can be no coalition," Mr Stephen added in a statement.
"We consistently stated to people across Scotland at all times during the campaign that this was our position and it will not change.
"In these circumstances it seems likely there will be a minority SNP government.
"The Scottish Liberal Democrats will work constructively to promote our positive policies in the new parliament."
Ms Sturgeon said: "The SNP is inviting the Liberal Democrats to get around the table to see if we can resolve the differences we have and build upon the things that we agree about.
"Scotland voted for a new government last Thursday and I think it is now incumbent on all parties to see if we can put together that new progressive coalition to take the country forward."
She said there had been informal talks between Mr Salmond and Mr Stephen in which the SNP leader had said there was scope for compromise on the independence issue.
The last eight years of the Scottish Parliament have seen Scotland run by a Labour-led coalition with the Liberal Democrats.
Earlier, Tavish Scott, who ran the Lib Dems' election campaign, said his party would not share power with Labour.