The country's rapid economic descent, which sent the jobless rate soaring to 26.26 percent, has been easing up since the start of the year, the Bank of Spain said in a monthly report.
"Available data, still partial and incomplete, would be coherent with a stabilization or even a slight increase in output in the July–September period," it said.
The rate of deterioration in various sectors of the Spanish economy had slowed, the central bank said, pointing to rising confidence among households and retailers, and a return to expansion in manufacturing.
Employment was still falling but at a slower pace, it said.
The report was the latest sign of greater official optimism about Spain's economy, the fourth-largest in the euro zone, which last year averted a widely anticipated full-blown economic bailout.
Prime Minister Mariano Rajoy this week said the government planned to raise its economic growth forecast for next year to 0.7 percent from 0.5 percent when it releases its budget for 2014 on Friday.
Rajoy told the Wall Street Journal that he expected the economy to grow by between 0.1 and 0.2 percent in the third quarter.
"Spain is out of recession but not out of the crisis," the newspaper quoted him as saying. "The task now is to achieve a vigorous recovery that allows us to create jobs."
Spain has been struggling in a double-dip recession brought on by the bursting of a housing bubble in 2008, which threw millions out of work, left banks holding huge bad loans and sent the public debt soaring.
Rajoy's right-leaning government is expected to stick to its austerity policies in the 2014 budget, freezing government workers' salaries and abandoning inflation-indexing for retirement pensions.
The government set itself the task of finding €150 billion ($200 billion) in savings between 2012 and 2014 as it battled to curb the public deficit and rein in the sovereign debt so as to calm global markets.
It plans to reduce the public deficit from 7.0 percent of economic output last year to 6.5 percent this year and 5.8 percent in 2014, eventually dipping below the European Union-agreed ceiling of 3.0 percent by 2016.
Moody's Analytics said Spanish banks, which have tapped €41.3 billion euros ($56 billion) from a eurozone rescue loan to clean up their balance sheets, would remain under pressure from their exposure to the plunging real estate sector.
"They will keep credit conditions tight rather than lowering cash dividends or issuing new shares to improve their capital ratios," Moody's predicted.
Spain's sovereign borrowing costs have dropped as concerns over its finances eased, it said.
"However, there is a risk that investors will start to worry about Spain," Moody's Analytics said.
"The weak recovery will keep a lid on tax revenue, making it difficult for the government to reduce its debt burden."