The auction will be held "before the summer", said Rajoy, addressing a climate change symposium in Madrid.
Rajoy's announcement follows the finalisation last week of Spain's second renewables power auction, in which wind power bagged over 99% (2.98GW) of the 3GW allocation.
A government statement said this third auction will redress the demand from renewables developers, who had put in bids for than than triple the capacity on offer in the second auction.
In that second auction, all winning bids had offered the maximum discount, effectively offering to produce at wholesale market prices with no subsidy.
The third round will be even more exacting, with bids competing on the basis of lowest installed capacity costs.
While the government sees the second auction's oversubscription as a sign of success, Spain's wind energy association AEE believes developers have no other options for advanced projects on hold, following a four-year moratorium on renewables.