Stagecoach's underlying pre-tax profit rose from £104.4 million to £105.6m for the six months to October 31 helped by a 40% rise in operating profit at its North American division, which includes yellow school bus services and Megabus coaches, to $30.6m (£19.6m).
This allowed it to announce a 2.9p interim dividend to be paid on March 5, up from 2.6p last year.
Meanwhile, Aberdeen-based FirstGroup dismissed as "flawed" demands from activist investor Sandell Asset Management that it sell its Greyhound bus arm and list its other North American interests on the stock exchange to pay down debt and invest in its UK business.
Stagecoach co-founder and chairman Sir Brain Souter said: "North America presents huge opportunities for the group. The current high proportion of travel by car means there is a significant potential market for our commuter and inter-city bus services."
While earnings from the US are just a quarter of those from its core UK bus business, Megabus has been expanding rapidly in recent years, in part in competition to the established Greyhound coach business FirstGroup bought in 2007. Stagecoach recently launched more Megabus routes in Atlanta and Memphis and plans to expand further in 2014.
In its UK bus business, which was without last year's £4m Olympic Games contract, a 1% rise in like-for-like passenger numbers led to a 0.1% rise in operating profit to £76.9m.
Stagecoach expects further economic growth to boost revenues but warned it could increase costs.
Finance director Ross Paterson said: "The biggest element of our cost base is labour. What we would expect to see is an acceleration in the rate of revenue growth and increased pressure on wages as the economy recovers and the wage rate recovers."
He added: "We do not expect the pressure on government spending to abate." Bus companies have been hit by reduced support for concessionary travel schemes.
Mr Paterson said the group plans to introduce more products for customers on its Citylink coach joint venture which has started running overnight services with flat beds to London and premium services with at-seat service during the day for services within Scotland.
"We believe this has exciting potential for markets in other countries," Stagecoach said.
Meanwhile, FirstGroup dismissed calls from Sandell, which owns 3.1% of the company, to sell its US operations which the investor claimed could boost shareholder value by 50%.
"The group has engaged with Sandell several times, reviewed their proposal in detail and believes that it is not compelling and contains a number of structural flaws and inaccuracies," FirstGroup said.
The group, which is seeking to turn around its own struggling UK bus business after a £615m cash call to preserve its investment grade credit rating, said its existing plans "will deliver superior value" to alternatives.
Tom Sandell, chief executive of Sandell Asset Management, 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.
"We will continue to engage with the company and invite other shareholders to discuss our proposals so that together, as responsible owners of this business, we can set it on the right path to long term success."
He said he backed the appointment of former Royal Bank of Scotland director John McFarlane as chairman in place of Aberdeen Asset Management chief executive Martin Gilbert.
But he said a break-up would enable FirstGroup to fund its bus investment programme and would put it in a strong position to bid for the next round of UK rail franchises.
City analysts reacted sceptically to the Sandell plans.
"You would want to sell against a backdrop of a strong US economy, not an improving one," Shore Capital analyst Martin Brown said.
Gerald Khoo, analyst at Liberum Capital, said: "We struggle to see how a strategy of large scale disposals creates value."
Shares in FirstGroup closed up 5.6p or 4.8% to close at 121.6p. Stagecoach shares closed up 10.2p or 2.8% at 372p.