* RBA deliberated for a very long time before holding rates - Stevens
* Aussie falls to fresh three-year low below $0.91
* Transition from mining investment boom challenging - Stevens (Adds comments on deliberations, market reaction)
SYDNEY, July 3 (Reuters) - The cooling of Australia's long-run mining investment boom will pose a significant challenge, but the central bank stands ready to help support an economy shifting to a new source of growth, the head of the Reserve Bank of Australia said on Wednesday.
Speaking just a day after the RBA left its cash rate unchanged at a record low 2.75 percent, RBA Governor Glenn Stevens said the board "deliberated for a very long time" before the decision.
That surprised markets, which had expected the decision to hold rates to be more clear-cut and helped knock the Australian dollar to its lowest level in three years.
Stevens noted that the non-resource sectors could not be guaranteed to strengthen on cue and to the right degree.
"The Reserve Bank, for its part, has a well-established monetary policy framework. Guided by this, we will be able to continue to do our part, consistent with our mandate, to assist the transition in sources of demand that is needed," he told a business lunch in Brisbane.
"We cannot fine-tune it - no one can promise that - but we will do what can reasonably be done."
The RBA has slashed its cash rate by a total of 200 basis points since late 2011. Its latest move was in May.
Stevens said with interest rates low, sectors such as housing and non-mining business investments should pick up in time.
He also said he was surprised by the resilience of the strong local dollar, but noted that free-floating exchange rates "do eventually adjust" and if the economy needed a lower exchange rate, it would probably get one.
The Australian dollar fell to a low of $0.9098, its lowest since September 2010, as markets priced in a better than 50 percent chance of a further cut in interest rates next month.
"The upshot is that the RBA was closer to cutting (interest rates) than we thought after yesterday's post-meeting statement," said Joseph Capurso, currency strategist at Commonwealth Bank of Australia.
The Aussie has fallen around 12 percent in the past two months on a trade-weighted basis, bringing relief to many exporters and the tourism sector. (Reporting by Ian Chua and Lincoln Feast; Editing by Eric Meijer)