"We expect to get back to sample-analysis science by the end of the week," said Curiosity mission manager Jennifer Trosper.
On February 28, controllers put the rover into "minimal activity safe mode" when they switched the machine's operations to a backup computer after detecting malfunctions in the primary computer's flash memory.
Engineers have diagnosed the software issue that prompted the alert last month, and are prepared to prevent it from happening again, NASA said.
The once-primary "A-side" computer is now back online as a backup, it added, and engineers are testing the B-side computer, which has taken over, by commanding a preliminary free-space move of the robotic arm.
The six-wheeled vehicle, with 10 scientific instruments on board, is the most sophisticated robot ever sent to another planet.
The $US2.5 billion Curiosity mission, which is set to last at least two years, aims to study the Martian environment and to hunt for evidence of water in preparation for a possible future manned mission.
Last week, NASA announced that the rover's analysis of a rock sample had found conditions once suited to life on the Red Planet.
"A fundamental question for this mission is whether Mars could have supported a habitable environment," said Michael Meyer, lead scientist for NASA's Mars Exploration Program. "From what we know now, the answer is yes."
The NASA team said this was the first definitive proof a life-supporting environment had existed beyond Earth.