The Liberal Democrats have ruled out a coalition deal with Labour in the Scottish Parliament.
Tavish Scott is one of 16 Lib Dem MSPs
The Lib Dems' Tavish Scott told BBC Scotland that if his party was not able to share power with the SNP, it would be on the backbenches.
The Nationalists, with 47 MSPs, are now the largest Holyrood party.
Meanwhile, the Scottish Green Party has agreed in principle to open talks with the Nationalists on the formation of a new government.
The Greens, who have two MSPs, said there was no barrier to co-operating with Alex Salmond's party and have not ruled out a formal coalition deal.
The two parties would have a combined strength of 49 MSPs - well short of the 65 required to command a majority at Holyrood.
Speaking on the Politics Show, Mr Scott ruled out working with Scottish Labour, as his party did in the pre-election coalition government.
But he said the key stumbling block was the SNP policy for a referendum on Scottish independence, which the Lib Dems, who have 16 MSPs, oppose.
"The SNP have to decide whether they want independence and for the next four years to be dominated by independence," said Mr Scott.
"They have to ditch the referendum."
The Nationalists will seek to "open informal discussions" with the Liberal Democrats over the coming days.
SNP deputy leader Nicola Sturgeon said: "We believe there should be a referendum with independence on the ballot paper, but beyond that we have said we will be as constructive as possible to try and put together a government in Scotland's best interests."
Meanwhile, First Minister Jack McConnell told BBC Scotland he "stands ready" to step in if the SNP is unable to form a government in Scotland.
The Scottish Labour leader said Mr Salmond and the SNP had the right to make the first move in attempting to form an administration.
If it failed, he said, Labour would then make its move.
The Greens and the SNP already agree on several policies - both support independence and are opposed to new nuclear power stations.
In separate statements, the two parties described their discussions as "positive and constructive".
The Nationalists, who won one more Holyrood seat in the election than Scottish Labour, said their aim was to establish a "progressive coalition".
Green co-leader Robin Harper was re-elected to Holyrood
An SNP, Liberal Democrat and Green coalition would have a single-seat majority in Parliament.
The situation may mean that Independent MSP Margo MacDonald could hold a crucial role in the formation of a new government, although she said she did not expect to be part of a coalition.
She also admitted to considering a bid to become the Scottish Parliament's next presiding officer.
"I will work with whoever, I believe, has got the best game plan for the good governance of Scotland and who is also able to disentangle the discussions we must have on our constitutional powers," she said.
Mr McConnell told BBC Radio Scotland's Sunday Live programme that the SNP had a responsibility to try to form a government.
"But it's far too early to tell, in this 28-day period in which we have the opportunity to form a new government in the Scottish Parliament, if they will succeed in doing that," he said.
"Alex Salmond has to show he is capable of and has the character to be the leader of a new government, if he is to form one.
"If he can't achieve that then the other parties in the parliament will need to consider what to do next."