Watch a series of animations from NASA showing how the asteroid retrieval mission might unfold.

By Alan Boyle, Science Editor, NBC News

NASA says it will begin work on an ambitious mission to capture a near-Earth asteroid and bring it to a stable orbit in the Earth-moon system as part of the agency's overall $17.7 billion agenda for the coming year.

The budget request for fiscal year 2014, unveiled on Wednesday, also aims to get U.S. astronauts back to flying on U.S.-based spaceships by 2017, launch the $8.8 billion James Webb Space Telescope by 2018 and send another rover to Mars by 2020.

The proposed budget is about $50 million less than the amount sought a year ago, but about $1 billion more than the agency's current spending plan. Billions of dollars would be set aside to continue operations on the International Space Station, keep up the work on interplanetary missions, expand the nation's network of Earth-observing satellites and upgrade aerospace technologies. However, the headline-grabber in the budget is the asteroid retrieval mission, which is budgeted for $105 million in spending during the fiscal year beginning in September.

"This mission represents an unprecedented technological feat that will lead to new scientific discoveries and technological capabilities and help protect our home planet," NASA Administrator Charles Bolden said in a statement accompanying the budget request.

Planning documents suggest that the space agency would launch a probe powered by a next-generation solar electric propulsion system sometime around 2017, to rendezvous with a 7- to 10-meter-wide (25- to 33-foot-wide) asteroid around 2019. A collapsible shroud would be wrapped around the asteroid, and then the probe would pull the space rock to a stable point in high lunar orbit or at a gravitational balance point beyond the far side of the moon.

Speaking on condition of anonymity, officials familiar with the plan told NBC News that NASA was already beginning the work to identify a candidate asteroid. The 2014 budget includes $78 million for planning the mission, and $27 million to accelerate NASA's efforts to detect and characterize potentially hazardous asteroids. NASA's chief financial officer, Elizabeth Robinson, indicated that this spending would come in addition to the $20 million that the space agency currently spends annually on asteroid detection.

The plan for the mission was formally unveiled less than two months after an asteroid streaked through the atmosphere and broke up over Russia. The breakup sparked a meteor blast that shattered windows and injured more than 1,000 people.

That asteroid was thought to have been about 17 meters (55 feet) wide. The type of asteroid targeted for the future NASA mission, in contrast, would be too small to pose a threat to Earth even if it were to break loose somehow and plunge through the atmosphere.

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NASA touts plan to grab asteroid as 'unprecedented technological feat'