The SNP has begun informal coalition talks after the party became the largest in the Scottish Parliament.
Alex Salmond said formal negotiations had still to take place
The election gave the Nationalists a total of 47 seats, beating Scottish Labour by just one seat.
Meanwhile, Labour extended a hand to other parties, but said it would not rush into making a judgement on forming the next Holyrood government.
Scottish Liberal Democrats and the Greens are considering whether or not to enter into discussions with the SNP.
The three parties would have a combined total of 65 seats - just enough to form a majority at Holyrood.
The Greens, who have at this stage ruled nothing in or out, would support the SNP's policy of a referendum on independence, but such a move would be opposed by the Lib Dems.
BBC Scotland's political editor Brian Taylor said the Liberals seemed to be feeling disinclined to do a deal of any sort after a "relatively bruising" experience at the polls.
Senior sources said the party may prefer to concentrate for now on rebuilding their own prospects outside government.
SNP leader Alex Salmond said his party had begun exploratory coalition talks.
"We've had conversations informally, but there's been no formal negotiations as yet," he said.
"During the election we expressed a preference for a coalition and that's certainly my preference."
In a statement agreed by Labour MSPs at a meeting in Glasgow, the party recognised the SNP's victory, but also claimed there was a large majority against Scottish independence.
"Scottish Labour stands ready to work with others who want to make devolution work," said the statement.
"We recognise our responsibilities to the people of Scotland and to those who voted Labour on Thursday. This election result demonstrates that the people of Scotland do not want separation to be Scotland's national priority."
A first minister has to be appointed within 28 days of the election
The statement went on to say: "Given the divided parliament and the uncertainty created, Scottish Labour recognises it would be wrong to make an immediate judgement about our stance on the next steps towards the formation of the next Scottish government."
The election left the Tories with 17 seats and the Lib Dems with 16.
There are two Green MSPs and one independent, Lothians list MSP Margo MacDonald.
Under the Scotland Act, a new first minister has to be appointed within 28 days of the election.
Scottish Liberal Democrat leader Nicol Stephen said that there was no way his party would support a referendum on independence.
"In terms of a potential coalition relationship with the Liberal Democrats, we've been very clear about this.
"We don't support independence. We don't support a referendum on independence. We support more powers for the Scottish parliament."
The Electoral Commission has launched an inquiry after the election was marred by technical problems, delays and a high level of spoiled ballot papers.
Trade and Industry Secretary Alistair Darling told BBC Radio 4's Today programme that he had concerns about the complexity of the voting system when he was Scottish secretary.