Compared to the second quarter of 2011, the nation's economic output fell 1.3 percent April through June, the institute said.
Both statistics show sharper declines than the first quarter, when the quarter-to-quarter decline was 0.3 percent and the year-over-year decline was 0.6 percent.
Employment in Spain was declining at an annual rate of 4.6 percent in the second quarter, also a sharper rate of decline than the first three months of the year, when employment was falling 3.6 percent year-over-year.
From the end of the second quarter of 2011 through the second quarter of 2013, the economy in Spain has lost 801,000 jobs, the report said.
The cost of labor based on production, called unit labor costs, was a 2.1 percent decline in the second quarter.
Spain is also struggling to put its banks back on solid footing after a decade of ill-advised property loans that are now dragging down the financial system with billions of dollars of bad loans on bank ledgers.
Spain is eligible for about $125 billion in international aid and is reported to be considering using $75 billion of that to shore up its banking sector.
Parliament is scheduled to act Friday on a proposal to create a so-called "bad bank," which would be a repository for bad loans that would be unwound over time, likely for steep losses.