WASHINGTON — To soar far away from Earth and even on to Mars, NASA has dreamed up the world’s most powerful rocket, a behemoth that borrows from the workhorse liquid-fuel rockets that sent Apollo missions into space four decades ago.

But with a price tag that some estimate at $35 billion, it may not fly with Congress.

NASA Administrator Charles Bolden and several members of Congress on Wednesday unveiled the Obama administration’s much-delayed general plans for its rocket design, called the Space Launch System. The multibillion-dollar program would carry astronauts in a capsule on top, and the first mission would be 10 years off if all goes as planned. Unmanned test launches are expected from Cape Canaveral, Fla., in six years.

Calling it the “largest, most powerful rocket built,” NASA’s exploration and operations chief, William Gerstenmaier, said the rocket will be tough to construct. But when NASA does it, “we’ll have a capability to go beyond low-Earth orbit like no other nation does here on Earth,” he said in a telephone briefing Wednesday.

The rocket resembles those NASA relied on before the space shuttle, but even its smallest early prototype will have 10 percent more thrust than the Saturn V that propelled Apollo astronauts to the moon. When it is built to its fuller size, it will be 20 percent more powerful, Gerstenmaier said. That bigger version will have the horsepower of 208,000 Corvette engines.

NASA is trying to remain flexible on where it wants to go and when. The space agency is aiming for a nearby asteroid around 2025 and then on to Mars in the 2030s. There could even be a short hop to the moon, but not as a main goal. All those targets require lots of brute force to escape Earth’s orbit, something astronauts have not done since 1972.

The far-from-finalized price tag may be too steep given federal budget constraints.