Sandell Asset Management wants Aberdeen-based FirstGroup to sell Greyhound and hive off its remaining US operations leaving the business focused on its UK bus and rail interests.
The plan was dismissed last month by FirstGroup, which said it was not compelling and contained a number of structural flaws and inaccuracies.
However, the hedge fund reiterated calls for a split yesterday, when it said: "Sandell urges the company to reconsider its premature rejection of the proposals. "
The New York-based business sent a letter to the FirstGroup board with a lengthy "White Paper" justifying its proposal.
It said the paper takes account of "relatively minor issues" raised by FirstGroup, which held talks with Sandell last year.
Sandell has a 3.1% stake in FirstGroup.
Chief executive Tom Sandell said: "We believe shareholders strongly support our ideas, and have been encouraged by their reaction since our engagement with the Company became public."
Its letter drew no response from FirstGroup, which set out a strategic plan to boost its long term performance in May.
The company raised £615 million to preserve its investment grade credit rating, in a discounted rights issue that month.
A source close to the company dismissed suggestions the board had rebuffed Sandell's suggestions prematurely.
"The company looked in detail at their proposals and considered them to be structurally flawed and with a number of inaccuracies," said the source.
FirstGroup management will discuss their own plans to increase profits and returns for shareholders at a capital markets day in the City on 23 January.
The session will feature an appearance by John McFarlane, the City heavyweight who succeeded Martin Gilbert as chairman of FirstGroup on 1 January.
Mr McFarlane has won plaudits for his work as chairman of Aviva, where he has overseen a programme to narrow its focus which included the sale of its US business.
On Tuesday FirstGroup announced Mr McFarlane had shown his confidence in its long-term prospects by choosing to receive his £250,000 annual fee in shares in the group.
He has committed to hold those shares for as long as he remains on the board.
Last month Sandell said its plan would allow FirstGroup to boost shareholder value by 50%
Sandell claims FirstGroup became too complex following the £1.9bn acquisition of America's Laidlaw in 2007.
Shares in FirstGroup closed up 0.4p at 141p.