The rover will set course to the drilling location in coming days to confirm results from the first drilling, NASA said.
This second drilling target, called "Cumberland," lies about 2.75 meters west of the rock where Curiosity's drill first touched Martian stone in February.
Curiosity took the first rock sample ever collected on Mars from that rock, called "John Klein."
The rover found evidence of an ancient environment favourable for microbial life. Both rocks are flat, with pale veins and a bumpy surface. They are embedded in a layer of rock on the floor of a shallow depression called "Yellowknife Bay."
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"We know there is some cross-contamination from the previous sample each time," said Dawn Sumner, a long-term planner for Curiosity's science team at the University of California at Davis.
"For the Cumberland sample, we expect to have most of that cross-contamination come from a similar rock, rather than from very different soil," Sumner said.
Although Cumberland and John Klein are very similar, Cumberland appears to have more of the erosion-resistant granules that cause the surface bumps.
Mission engineers at NASA's Jet Propulsion Laboratory (JPL) in Pasadena, recently finished upgrading Curiosity's operating software following a four-week break.
The rover continued monitoring the Martian atmosphere during the break but the team did not send any new commands because Mars and the sun were positioned in such a way the sun could have blocked or corrupted commands sent from Earth.
After the second rock drilling in Yellowknife Bay and a few other investigations nearby, the rover will drive toward the base of Mount Sharp, a 5-kilometre tall layered mountain inside the crater.