Media playback is unsupported on your device Media caption Watch the launch from Cape Canaveral

The head of Nasa has hailed a "new era" in exploration after the launch of the first cargo delivery to the space station by a private company.

The Falcon rocket, topped by an unmanned Dragon freight capsule, lifted clear of its Florida pad at 03:44 EDT (07:44 GMT; 08:44 BST).

The launch system has been built by California-based firm SpaceX.

The initial climb to an altitude some 340km above the Earth lasted a little under 10 minutes.

Within moments of being ejected, Dragon opened its solar panels.

It also unpacked its navigation equipment.

Nasa's administrator Charles Bolden said: "Today marks the beginning of a new era in exploration... The significance of this day cannot be overstated; a private company has launched a spacecraft to the International Space Station that will attempt to dock there for the first time.

"And while there is a lot of work ahead to successfully complete this mission, we are certainly off to good start."

It will take a couple of days to reach the station. The plan currently is for the vessel to demonstrate its guidance, control and communications systems on Thursday, at a distance of 2.5km from the International Space Station (ISS).

If those practice proximity manoeuvres go well, Dragon will be allowed to drive to within 10m of the station on Friday. Astronauts inside the platform will then grab the ship with a robotic arm and berth it to the 400km-high structure.

They will empty Dragon of its 500kg of food, water and equipment, before releasing it for a return to Earth at the end of the month.

For Elon Musk, the CEO and chief designer at SpaceX, Tuesday's lift-off was a special moment.

"Every bit of adrenalin in my body released at that point," he told reporters. "There's so much hope riding on that rocket, so when it worked, and Dragon worked and the solar arrays deployed, [company employees] saw their handiwork in space and operating as it should - it was tremendous elation. It's like winning the Superbowl."

The mission has major significance because it marks a big change in the way the US wants to conduct its space operations.

Nasa is attempting to offload routine human spaceflight operations in low-Earth orbit to commercial industry in a way similar to how some large organisations contract out their IT or payroll.

The carriage of freight will be the first service to be bought in from external suppliers; the transport of astronauts to and from the station will be the second, later this decade.

The US space agency hopes these changes will save it money that can then be invested in exploration missions far beyond Earth, at destinations such as asteroids and Mars.

Image caption SpaceX mission control celebrates a successful ascent to orbit for Falcon and Dragon

SpaceX has many new systems it has to demonstrate in the coming days, and has tried to lower expectations ahead of the mission, repeating often that its aim is to learn things it did not previously know.

Nasa has set the California company a series of development milestones. Only when those have been met fully will a $1.6bn ISS re-supply contract kick in.

The agency is also looking to engage a second cargo partner. Orbital Sciences Corporation of Virginia is slightly behind SpaceX in its development schedule, although it started work on its Antares rocket and Cygnus capsule system later. Orbital expects to fly a first mission to the vicinity of the ISS later this year or early in 2013.

"We're really at the dawn of a new era in space exploration, and one where there's a much bigger role for commercial space companies," Mr Musk said.

"I think perhaps there's some parallels to the internet in the mid-90s where the internet was created as a government endeavour but then the introduction of commercial companies really accelerated the growth of the internet."

Image caption Out with the old: Since the retirement of the shuttles last year, the US has relied on other ISS partners for cargo and crew transport

Tuesday's Falcon launch was also notable for the small and rather unusual payload that piggy-backed the ride to orbit.

This was a container holding the cremated remains of more than 300 space enthusiasts, among them the late Star Trek actor James "Scotty" Doohan.

The ashes had been placed in the Falcon's discarded second stage.

They will continue to circle the planet for about a year before falling back to Earth and vaporizing.

Jonathan.Amos-INTERNET@bbc.co.uk and follow me on Twitter