The US is already the world's largest food donor.
Nancy Pelosi, the House of Representatives speaker, pledged in a statement that legislators "will respond rapidly to the growing urgent need for international food assistance", though she did not explicitly mention Bush's request.
Bush also used his speech to stress the importance of removing trade barriers as a way to combat the rising prices.
He emphasised the importance of concluding the "Doha Round" of global trade talks - which have stalled amid disputes over commodities - and called for countries to remove barriers to crops produced through biotechnology.
"These crops are safe, they're resistant to drought and disease, and they hold the promise of producing more food for more people," he said.
Bush said the US was on track to spend nearly $5 billion in 2008 and 2009 to battle global hunger, and stressed that other wealthy countries also needed to step up their contributions.
The proposed food aid comes just weeks after Bush approved the release of 250,000 tonnes of wheat from an emergency crop trust, a step the US last took in 2005.
Administration officials said the $770m, which would be budgeted for 2009 and requires approval from Congress, would include $395m in emergency food aid, $225m for food vouchers, seeds, or aid purchases in the developing world, and $150m for development work aimed at food security.
The World Bank has estimated that a doubling of food prices over the past three years could push 100 million people in poorer developing countries further into poverty.
The increase in food prices is typically blamed on a number of factors, including rising food consumption in emerging economies like India and China and adverse weather.
The growing use of food crops to make biofuels like ethanol is also seen as a driver, although some argue the fuels only account for a small share of the price spike.