By Keith Weir

BERLIN (Reuters) - Germany's president has warned that there are limits to how many refugees his country can absorb as it prepares for as many as 800,000 arrivals this year, showing growing concern even at the highest level over how to look after so many newcomers.

"We want to help. We have a big heart. However, there is a limit to what we can do," President Joachim Gauck, a former rights activist in communist East Germany, said in a speech on Sunday evening.

"Our ability to take in people is limited, although we don't know yet where those limits are," he added.

The comments from the head of state, who has a largely ceremonial role but whose words carry moral authority, appeared to be striking a more cautious tone than Chancellor Angela Merkel who has said Germany can cope with the record influx.

The government declined to respond directly to Gauck's comments, reflecting political convention, but defended its handling of the situation.

"The German government and the chancellor are convinced that protection has to be given to those who need it, whether they are persecuted for political reasons or fleeing war," said government spokesman Steffen Seibert.

The debate came amid signs of growing tension among asylum seekers, part of a wave of mass migration into the European Union from the Middle East and parts of Africa.

Fourteen people were injured on Sunday when a brawl broke out between two rival groups in a refugee center in the western German town of Calden, police said. The refugees were being housed in tents set up on a disused airfield.

A union representing German police officers has suggested that refugees should be divided according to their religion to try to reduce the risk of conflict.

Germany has reintroduced border controls with EU neighbors to try to regulate the flow of people after initially throwing open its doors to refugees from Syria.

The central government also agreed last week to give its 16 regional states around 4 billion euros ($4.5 billion) next year to help cover the cost of looking after refugees.

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"The German government stands by its decision to now introduce signs of order into the process for the arrival and the admission of refugees," Seibert added.

Merkel's popularity has dropped sharply over her handling of the refugee crisis, two polls showed at the weekend, indicating a shift in the mood in the Europe Union's most populous country.

(Additional reporting by Tina Bellon; Editing by Noah Barkin and Alison Williams)