BRUSSELS (Reuters) - The euro zone economy grew at the same slow pace in the third quarter as the second and core inflation dipped in October, reinforcing expectations that the European Central Bank will decide to extend its asset-buying program in December.

The European Union's statistics office Eurostat said gross domestic product in the 19 countries sharing the euro rose 0.3 percent quarter-on-quarter in the July-September period and by 1.6 percent year-on-year.

Both figures were the same as in the second quarter and matched expectations of economists polled by Reuters.

Consumer prices rose 0.5 percent year-on-year in October, Eurostat estimated, picking up from 0.4 percent in September and 0.2 percent in August as the drag on the index from energy diminished.

Energy prices were only 0.9 percent lower in October than 12 months earlier, compared to 3.0 percent down in September.

However, excluding the most volatile prices for unprocessed food and energy, inflation was just 0.7 percent year-on-year, down from 0.8 percent in the previous five months. The figure is the one the ECB uses as core inflation.

The European Central Bank wants a higher rate of overall inflation -- close to 2 percent over the medium term -- and has been buying euro zone government bonds to inject cash into the banking system and make banks lend to the real economy.

The ECB meets in December and will have to decide then whether it extends its bond-buying beyond an initial target date in March. To do otherwise would essentially subject markets and banks to a cold turkey cut-off.

ECB policymakers have said accommodative monetary policy would be maintained until inflation is on a sustainable path to the target. ECB Executive Board member Benoit Coeure said on Friday on growth: "The whole discussion will be how sustained is that."

In fact, euro zone sentiment, published by the European Commission on Friday, was much better than expected in October driven by higher optimism in industry and services, suggesting a robust start to the fourth quarter.

However, Capital Economics said it doubted this would be enough to convince the ECB to slow the pace of its asset purchases yet.

"Indeed, we still expect the Bank to announce a six-month extension of the program at the current pace to September 2017 at its December meeting," it said.

Howard Archer, chief European economist at IHS Markit agreed, although said it was conceivable that the ECB could announce a lower rate of purchases after March.

"Even if euro zone growth does show further signs of improvement over the coming weeks, there is a compelling case to try and fuel the improvement given past hiccups," he said.

(Reporting By Jan Strupczewski and Philip Blenkinsop)