"Here, the policy has been less binding - particularly after the policy was relaxed somewhat in 2013, but also because wealthier people generally want fewer children," the bank said. "But it all helps at the margin."
The Chinese Communist Party's Central Committee said in a statement that the decision was "to improve the balanced development of population" and to deal with an aging population.
The official Xinhua News Agency said the proposal must be approved by the top legislature before it is enacted, which is essentially a formality. It gave no indication of when that would happen.
The move may not spur a huge baby boom, however, in part because fertility rates are believed to be declining even without the policy's enforcement.
Previous easings of the one-child policy have spurred fewer births than expected, and many people among China's younger generations see smaller families as ideal.
China, which has the world's largest population at 1.4 billion people, introduced the one-child policy in 1979 as a temporary measure to curb a then-surging population and limit the demands for water and other resources. Soon after it was implemented, rural couples were allowed two children if their firstborn was a girl. Ethnic minorities are also allowed more than one child.