New York-based Sandell Asset Management, the owner of 3.1% of the company, wants Aberdeen-based First to offload its inter-city bus service Greyhound and spin off the rest of its North American arm, which includes school bus services for six million students.
It believes the changes will strengthen its balance sheet and better prepare the company for the upcoming round of UK rail franchise bids, as well as enabling it to invest in the turnaround of its UK bus arm.
FirstGroup has engaged with Sandell several times but said the proposals were not compelling and contained structural flaws.
It said it is committed to existing plans announced in May under which it will pour £1.6 billion into a four-year investment programme and tackle debts of nearly £2 billion. The strategy will look to improve the performance of all divisions, including its GreatWestern rail arm.
The company, which is due to provide investors with more details of its plans on January 23, said: "We remain focused on the vigorous execution of our strategy."
Shares rose 3% today after Sandell said it would lobby other shareholders to support proposals that it believes will set the company "on the right path to long term success".
Chief executive Tom Sandell said: "Our established track record in company analysis and our sector expertise tells us that FirstGroup can turn around its historic poor performance by focusing on its UK rail and bus businesses."
FirstGroup's recent difficulties stem from the botched tender process for the West Coast mainline franchise, causing its takeover from Virgin to be put on hold and decisions on other rail operations to be delayed.
The company, which recently tapped investors for £615 million and cancelled its dividend, has warned that its turnaround plans required "hard work and persistent delivery" for some time to come.