All divisions except its London bus arm grew like-for-like revenue in the 12 weeks to July 21 this year.
The London division slipped 0.6% but Stagecoach suggested the result was in line with expectations.
Revenue is predicted to grow in London over the coming months as the impact of nine new contracts begins to filter through.
Across its other operations regional UK bus revenue grew 4.5%, UK rail increased 6.5%, North America was ahead by 5.7% while the joint venture Virgin Rail Group was up 5.8%.
The budget Megabus service in North America is now the fastest growing part of the group and saw its revenue soar 21.8% in the three months to the end of July.
Stagecoach said: "This reflects further growth in existing services, as well as contributions from our Texas and California networks launched during 2012/13.
"Overall, the North American business remains on track to deliver a significant step up in its operating profit in 2013/14 when compared to 2012/13."
The Twin America sightseeing business in New York saw a fall in revenue because of an "increasingly competitive" market.
Passenger volumes on UK regional buses increased year on year which Stagecoach believes may have been because of better weather persuading people to leave cars at home.
It said the strongest revenue growth was coming through passengers which have to pay full fares with concessionary, tendered and school revenues increasing at a slower rate.
Stagecoach said UK rail revenue has dropped back since July 21 partly because of the impact of the London Olympic and paralympic Games last year.
Discussions with the Department for Transport (DfT) over extensions to Stagecoach's South Western Trains and East Midlands Trains franchises are ongoing.
The company said it is still in the running for the Thameslink and Docklands Light Railway with the winning bidders to be announced in spring next year.
Virgin Rail Group and the DfT are continuing to discuss revised commercial terms which would see the company take a greater revenue and cost risk for running services on the West Coast Main Line through to April 2017.
At the moment Virgin Rail Group earns a fee equivalent to 1% of revenue with the DfT taking the risk that revenue or costs differ from those predicted.
Stagecoach shares closed up 20.4p at 327.8p.