It previously had a $2000/oz forecast for 18 months' time.
The bank said like the gold price, the size of major central bank balance sheets had been stable over the past decade at 21% to 28% of GDP.
The upgrade was prompted by the doubling of balance sheets and rise in fiscal deficits as countries try to stimulate economies to mitigate the impacts of the pandemic.
Bank of America believes US GDP could drop 30% this year, the steepest drop in modern history, while Japan's could decline by 21.8%.
"As economic output contracts sharply, fiscal outlays surge, and central bank balance sheets double, fiat currencies could come under pressure. And investors will aim for gold," the bank said.
"Hence, we mark-to-market our forecasts and now project an average gold price of $1695/oz in 2020 and $2063/oz in 2021."
Spot gold was trading at $2687/oz this morning, while futures were just over $1700/oz.
Bank of America sees a strong US dollar, falling equity market volatility and weak jewellery demand as potential headwinds.
BMO Capital Markets analyst Colin Hamilton told the World Gold Forum this week that jewellery demand could drop by 10% in 2020.
"A 10% demand drop would be the biggest in recent history," he said.
Still, Hamilton was extremely bullish on gold.
"2020 has a very precious-positive backdrop," he said.
Hamilton said macro asset allocation was crucial for gold in 2020, but also ETF flows.
"ETF flows are crucial to gold price formation," he said.
Gold ETF inflows had already reached 10 million ounces so far this year.
"This is likely to be a record year for gold ETF inflows," Hamilton said.
He tipped the US dollar to have limited influence on gold prices for the time being.
"Safe haven buying is ruling all."
Hamilton said gold producers were in the best shape they'd been in for many years after cleaning up balance sheets.
In January 2016, when the gold price was $1100/oz, the weighted average of companies covered by BMO was negative 4.4%.
"Fast forward to today, everyone's making very good margin now over all-in sustaining costs, but the key difference is free cashflow yield, on average, is now plus 5%," Hamilton said.
"So 5% still lags many other companies in the materials sector. I'd highlight the big iron ore miners, the big copper miners and even, the key oil and gas majors, they're still generating better free cashflow yields than that."
Hamilton said continuing to improve free cashflow generation over the coming years was key to attracting generalist investors.
"Gold is starting to screen well again in terms of the equity performance, but we really need to see consistency in that free cashflow generation, and returns to shareholders, to get a wider asset base and a wider investor interest coming through," he said.
Hamilton said foreign exchange moves and declining oil prices were playing into gold miners' hands.
"With that, it should be a very profitable year - it's up to the industry to really sustain those margins."