"If we do not act to curb climate change immediately, we will leave our children and grandchildren with an unrecognizable planet," bank President Jim Yong Kim said at Georgetown University.
"It is the poor -- those least responsible for climate change and least able to afford adaptation -- who would suffer the most," he said.
But an average global warming of 4 degrees Celsius, or slightly more than 7 degrees Fahrenheit, later this century could raise sea levels up to 5 feet, "putting more than 360 million city dwellers at risk," he said, citing a World Bank report.
"Drought-affected areas would increase from 15 percent of global cropland today to around 44 percent, with sub-Saharan Africa especially hard hit," he said. "Extreme weather events would occur with devastating frequency, with untold costs in lives and dollars."
But paradoxically, he said, humanity has an "opportunity to create a world free from the stain of poverty" by 2030, due in part to developing economies rebounding quickly from the global economic crisis.
These economies -- the bank's core "customers" for its loans and programs -- are also economically more stable due to stronger laws and increased investments in human capital and infrastructure, he said.
"We are at an auspicious moment in history when the successes of past decades and an increasingly favorable economic outlook combine to give developing countries a chance -- for the first time ever -- to end extreme poverty within a generation," he said.
"Our duty now must be to ensure that these favorable circumstances are matched with deliberate decisions to realize this historic opportunity," he said in his address Tuesday.
Kim cited several "courageous politicians" who committed to ending poverty in their countries, including Brazilian President Dilma Rousseff and Malawian President Joyce Banda.
"These bold calls demand action. The World Bank Group will be a relentless advocate and a loyal partner in encouraging policymakers to follow through on their promises to the poor," he said.
The bank defines extreme poverty as the 1.3 billion people living on less than $1.25 a day.
He called on nations "to enhance inclusiveness and curb inequality, and ensure that growth translates into poverty reduction, most importantly through job creation."
"To reach the 2030 goal, we must halve global poverty once, then halve it again, and then nearly halve it a third time -- all in less than one generation," Kim said.
This goal is ambitious but "within our grasp," he said.