AFP/File Wang Zhao
The world's most populous country has restricted most families to a single child since the late 1970s, but the Communist party said in November that couples would be allowed to have two offspring so long as one of the parents was an only child, rather than both.
Authorities had expected the change to result in more than 2 million extra births a year, but out of more than 11 million couples eligible, only 700,000 had applied for permission by the end of August, the China Daily newspaper said, citing the National Health and Family Planning Commission.
Of those, 620,000 had been authorized, it added.
China has a population of 1.36 billion, the National Bureau of Statistics said in January, but its working-age population fell by 2.44 million last year.
Over-60s accounted for 14.9 percent of the total, it said, and projections show that they will represent one in four of the population - 350 million people - by 2030.
The lower-than-expected desire to have more children might reflect changing perceptions of reproduction, particularly in cities, said Lu Jiehua, a demography professor at Peking University, according to the report.
The new policy affects mostly couples in urban areas, where the family-planning policy has been implemented more strictly than in the countryside.
But education and housing are expensive in cities, and reliance on children in old age is lower, making multiple offspring less necessary.
Chinese academics have called for an across-the-board two-child policy to be introduced to tackle emerging labor shortages.
China's birth-limit policies have at times been brutally enforced, with authorities relying on permits, fines, and, in some cases forced sterilizations and late-term abortions.
Beijing says the policy prevented food shortages and laid the foundations for the country's recent economic growth.