BERN (Reuters) - Climate protection is very important for the Swiss National Bank, but the issue should be tackled by politicians rather than central banks, SNB Chairman Thomas Jordan said on Friday.

"It is also important... we are serious and do not give the impression that we can solve all the problems of the world with monetary policy," Jordan told the SNB's shareholder meeting.

Environmental groups mounted a protest outside the event in Bern, demanding the SNB offload its investments in companies which they say are linked to global warming and climate change.

The SNB already had exclusion criteria in its investments, no longer holding stakes in coal-producing companies, Jordan said, noting that it was important the central bank did not implement policy which may not have popular support.

"It is the democratically legitimized authorities that are actually able or responsible to make these decisions. Parliament, government and so on," he said.

"They can introduce management tasks, emissions trade or subsidies. This is not the task of the National Bank."

Instead, the SNB worked better with a narrow mandate which focused on price stability, Jordan said.

(Reporting by John Revill; Editing by Dave Graham)