Rescuers on Wednesday had pulled the bodies of two boys and a girl from the rubble from Monday's disaster, caused when the rink's roof collapsed under heavy snow.
Of the 15 victims -- rescuers do not expect to find anyone else in the debris -- 12 were children or teenagers. The other three victims were women aged around 40.
Pope Benedict XVI, who was born in the state of Bavaria where the accident happened, sent a telegram to the archbishop of Munich on Wednesday to convey his condolences.
He said his thoughts were with relatives "after this tragic accident which cost the lives mostly of children," and wished the injured a speedy recovery.
Rudi Zeif, the fire chief in Bad Reichenhall, vowed that the search, with the help of sniffer dogs and cranes, would go on until the last of the missing had been recovered.
"We wanted to save people but we keep finding bodies. The worst is that so many are children," Mr Zeif said.
Hubertus Andrae, the police chief of the nearby town of Traunstein, said a third body found on Wednesday was a girl, after the two boys had been pulled out earlier.
The town has also set up an Internet-based book of condolences, which has so far been signed by more than 2,300 people from across the country, and by people from as far afield as Australia, Portugal and the United States.
Thirty-four people were also hurt when the roof collapsed. Thirteen of them were still in hospital but their lives were not in danger, German radio said.
It was not immediately clear what caused the flat roof of the building to cave in, in a region where heavy snowfall is commonplace.
Der Tagesspiegel newspaper on Wednesday cited meteorologists as saying there must have been about 180 tonnes of snow on the roof when it gave way.
State prosecutor Helmut Vordermayer has said evidence was being collected and a probe into the accident had been opened.
The events leading up to the collapse of the roof remained unclear on Wednesday.
The coach of a local ice hockey club, Thomas Rumpeltes, has said he was told the snow was to have been cleared from the roof shortly before it caved in.
Mr Rumpeltes said he had cancelled a practice at the rink for a youth team because the authorities had told him of the impending clearance shortly before the accident.
He said no one had warned of any risk of the roof being unstable and that the snow removal was only a precautionary measure.
The town's mayor Wolfgang Heitmeier has rejected accusations of negligence for allowing the rink to remain open, saying the roof had been examined hours before it collapsed and the amount of snow on it was within safety limits.
He rejected speculation that the authorities knew of structural problems, saying he "could not explain" what caused the collapse.
Bavaria's regional interior ministry on Wednesday rejected calls for safety certificates for buildings, saying the cause of the accident needed to be determined before measures could be taken.