By Michael Nienaber and Paul Day

BERLIN/MADRID (Reuters) - German inflation picked up in September to reach its highest level in 16 months and Spanish consumer prices rose for the first time since May 2014, positive signs for the European Central Bank that its ultra-loose monetary policy is working.

The ECB has unleashed unprecedented monetary stimulus in recent years to boost the economy and fight off the threat of deflation. It has cut interest rates aggressively to zero or less and pumped more than a trillion euros into the economy through asset purchases.

But with growth in the euro zone still moderate and inflation in the 19-member currency bloc barely above zero - well short of the ECB's target of nearly 2 percent - the central bank's critics say its monetary policy has reached its limits. Others say it should print even more money.

But Thursday's number offered some respite for the policymakers.

"Hooray, the prices are rising! This might sound crazy but it fits. Because the price development shows that the risks of deflation have been averted for now," KfW Bank economist Joerg Zeuner said.

The ECB has been concerned about a damaging deflationary spiral in the euro zone in which consumers delay purchases in expectation of lower prices, hitting economic growth.

Zeuner said he expected the German inflation rate -- which is something of a key to euro zone inflation as a whole -- to reach nearly 2 percent at the beginning of next year.

"Given a similar development in the euro zone, this will enable the ECB to aim for a smooth exit from its bond-buying program in 2017," he added.

German consumer prices, harmonized to compare with other European countries (HICP), rose by 0.5 percent on the year in September after an increase of 0.3 percent in August, the Federal Statistics Office said. This was the highest rate since May 2015 and in line with a Reuters consensus forecast.

On a non-harmonized basis, German inflation picked up to 0.7 percent on the year after 0.4 percent in August, it said.

Energy prices remained the main drag on the headline figure, but fell less sharply than in the previous months, a breakdown of the non-harmonized data showed. Costs for rents increased faster than in August while food inflation slowed.

RISING RENTS

The strong German inflation data came after Spanish EU-harmonized consumer prices rose by 0.1 percent year-on-year in September, the first increase since May 2014.

Spain's national consumer price index rose by 0.3 percent in September on an annual basis, up from a 0.1 percent drop in August and the first time it has risen since July 2015, the National Statistics Institute (INE) said.

ING economist Geoffrey Minne called the Spanish inflation data "a sign that ECB policy might be working after all".

But he added that overall euro zone inflation was still far away from the ECB's target of nearly 2 percent. "In that regard ECB monetary policy is likely to remain easy for some time to come," Minne said.

For the overall euro zone, economists polled by Reuters expect the inflation rate, due on Friday, to edge up to 0.4 percent in September after a rise of 0.2 percent in August. This would be the highest reading since October 2014.

In Berlin, leading economic institutes urged the ECB to wait and weigh the effects of its bond-buying program before taking more expansionary steps. But they also added that the ECB should take more measures if inflationary pressures remained weak.

On Wednesday, European Central Bank President Mario Draghi rejected German criticism that sub-zero interest rates were impoverishing savers and straining top lender Deutsche Bank <DBKGn.DE>, saying its monetary policy was a necessity to get the euro zone back on the path to growth and revive inflation.

Questioned by lawmakers who say ECB policy has damaged the euro zone and fueled the rise of right-wing populists, Draghi said Germans were actually net beneficiaries of the euro zone central bank's easy stance and the nation's bank troubles were actually due to poor efficiency.

(Additional reporting by Joseph Nasr and Reinhard Becker in Berlin; Writing by Michael Nienaber Editing by Jeremy Gaunt.)