The SpaceX Falcon 9 rocket blasted off from Cape Canaveral, Florida, early Tuesday carrying the first private spacecraft bound for the International Space Station. The rocket -- with its Dragon capsule filled with food, supplies and science experiments -- blazed into the predawn sky, avoiding the glitch that had caused its initial launch Saturday to be aborted a half a second before liftoff. That first attempt at launching the rocket was halted when a flight computer detected "high pressure in the engine 5 combustion chamber," according to the company. "During rigorous inspections of the engine, SpaceX engineers discovered a faulty check valve on the Merlin engine," the company said in a statement Monday. "The failed valve was replaced on Saturday, and after thorough analysis, the vehicle has been cleared for launch." The mission is designed to establish whether SpaceX can deliver cargo to the space station. It is one of a handful of private companies receiving funds from NASA with the goal of ferrying cargo into orbit. "It is a joint effort. I have to congratulate the SpaceX team for the absolutely incredible job that they've done in getting to this point," NASA Administrator Charles Bolden said. "You know this is the first step." NASA and SpaceX envision the unmanned Dragon docking at the station, where the crew will pull food, water and other provisions from the capsule. The launch Tuesday is one of 12 planned SpaceX flights to the International Space Station. It is the first time the Dragon capsule has been launched with the components needed for docking at the space station. SpaceX had previously test-launched the rocket. The current mission had been delayed several times because of problems with flight software. SpaceX hopes the experience with the cargo flights will help it reach its goal of carrying astronauts aboard the Dragon. NASA is currently reliant on the Russian space agency to ferry U.S. astronauts to orbit, since the retirement of the U.S. shuttle fleet has left the United States with no way to lift humans into space. "What's really important is not control, as much as it is the fact that the United States will once again be in the lead, will be providing our own vehicles to take our own astronauts and cargo to the International Space Station," Bolden said. "It's fine to rely on partners, but that's not where the greatest nation in the world wants to be." A White House official applauded the launch. "Every launch into space is a thrilling event, but this one is especially exciting because it represents the potential of a new era in American spaceflight," said John P. Holdren, the White House science adviser. "Partnering with U.S. companies such as SpaceX to provide cargo and eventually crew service to the International Space Station is a cornerstone of the President's plan for maintaining America's leadership in space."