The Aberdeen-based group says current bids to renew its £6billion ScotRail franchise and land the even more lucrative East Coast territory only represent "part of the pipeline of 14 major UK rail franchise opportunities" over the medium term.
The group said it was in negotiations over extensions of its existing Great Western and Trans-Pennine franchises.
The UK's biggest rail operator has so far lost its Caledonian Sleeper contract to Serco, its previous (First Capital Connect) share of a new Thameslink super-franchise to a consortium of Go-Ahead and French group Keolis, and the modest Essex Thameside franchise to National Express.
FirstGroup was updating the market with an interim management statement which assured that it was on track to meet its targets across all its US and UK businesses.
It noted that First ScotRail was planning "the most extensive train timetable that Scotland has ever seen" in support of this month's Commonwealth Games in Glasgow, while its buses would be transporting athletes, officials, media and sponsors and providing extra shuttle services for spectators.
The group said: "Our UK rail division delivered a robust performance with like-for-like passenger revenue increasing by 6.6 per cent in the period (first quarter). In the recent National Passenger Survey all of our train operating companies saw steadily increased customer satisfaction ratings, with First ScotRail and First Hull Trains recording their highest ever scores."
FirstGroup said its UK bus business had achieved increases of 2.7 per cent in the first quarter in both revenues and passenger volumes as its transformation programme in big cities, including Glasgow, kicked in.
It said: "Mobile ticketing has been introduced on our networks in Aberdeen, Worcester and Manchester and we are on track to complete the roll out of mobile ticketing systems nationwide by December 2014.
"While there is still some way to go, we are delivering our plan as forecasted to restore double digit margins to UK Bus by 2017."
At its biggest business, First Student in the US, the group said it was encouraged by the progress of contract repricing which was at the upper end of its plans, adding it had "also secured additional business through newly outsourced contracts as well as contracts won from competitors" in a largely supportive underlying market.
It expects the proportion of low margin contracts at that division to be below 30 per cent in this financial year, from 36 per cent in the previous one.
The First Transit business was continuing its strong financial performance while Greyhound, the iconic coach network, was now showing improved revenue trends helped by a more stable US economy.
Tim O'Toole, chief executive, said: "Trading during the first quarter was in line with our expectations and our transformation programmes are on track.
"Across the group we are confident that we have the right programmes underway to build on our market-leading positions and improve performance to create sustainable value over the medium term and beyond."
Panmure Gordon analyst Gert Zonneveld kept a hold rating on the FirstGroup stock citing the steady turnaround progress and margin improvement initiiatives at First Student and UK Bus.
FirstGroup shares, which were at 98p a year ago in the wake of its £615 million rights issue, and peaked this year at 146p in March, were up 2.4p, or two per cent, at 128.1p.