June 21 (Reuters) - BofA Merrill Lynch said an investment demand required to sustain gold prices in a range of $1,500-2,000 per ounce could be feasible in the next five years.

The brokerage believes investment has had a critical influence on the gold market and investor buying is the key to its long-run supply and demand balances.

"We look at supply and demand balances required to clear the gold market under three average price scenarios (i.e. $1,000/oz, $1,500/oz and $2,000/oz over the coming five years)," BoFA said in a note to clients.

The brokerage said gold prices above $2,000 or below $1,000 per ounce were not sustainable.

Sustaining a medium-term average price for the metal at around $2,000/oz looked challenging, BoFA said.

"In our view, to push gold above this level would require a disorderly sovereign default in the Eurozone or QE3 in the US, both of which are not our base case at the moment," the brokerage said.

Meanwhile, a decline in gold prices below $1,000/oz would lead to a sharp pick-up in fabrication demand, BoFA said. (Reporting by Soma Das in Bangalore; editing by James Jukwey)