The Prime Minister's intervention, so early in new Scottish Parliament, will infuriate Labour politicians north of the border, who were promised autonomy from Westminster.
It will also create tension with the Liberal Democrats, with whom Labour is hoping to form a coalition in the Parliament.
During the conversation, Mr Ashdown told Mr Blair not to meddle in Scottish politics. He warned that any Scottish coalition should be negotiated by Donald Dewar, Scotland's First Minister in waiting, and Jim Wallace, the Liberal Democrat's Scottish leader.
The Prime Minister also faces growing criticism from his own politicians for interfering. Malcolm Chisholm, one of Labour's new MSPs, yesterday warned the London party to keep out of Scottish politics. "Devolution is about people in Scotland making the decisions," he told the BBC.
Mr Blair's official spokesman said the Prime Minister was "kept well informed" of the negotiations - although Mr Dewar was officially in charge. "The Prime Minister continues to be the Prime Minister of the United Kingdom, therefore he has kept a role in the running of Scotland, Wales and Northern Ireland as well as England."
The Liberal Democrats are concerned that Downing Street will try to set the terms of any deal reached between the two parties. They are privately furious that the Chancellor and his team of advisers have remained in Scotland during the first crucial days of negotiations.
The critical issue for a coalition deal in Scotland is tuition fees for students, which Liberal Democrats want to scrap. Mr Dewar, confronting a majority in the new Scottish Parliament in favour of ditching the fees, is believed to favour a compromise.
He is prepared to offer at least two seats in the new Executive to the Liberal Democrats, including one for Mr Wallace.
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