The government has been pushing for fathers to take paternity leave as Japan faces a demographic crisis, yet a new wrinkle has emerged: Almost one-third of mothers report that their partners do little to help out around the house while they’re off work.

Of 508 mothers, 32 percent said their husbands did less than two hours of housework or child care per day during paternity leave, according to a survey released Wednesday by Mamari, a motherhood information portal. About 20 percent of the mothers reported that their husbands did more than eight hours of work.

The responding mothers said they often ended up doing housework themselves or that their husbands used some of the time to have fun.

The gender imbalance of household duties in Japan has received worldwide attention.

While 71 percent of women age 15 to 64 today have paying jobs, compared with 60 percent in 2012, men’s contributions in the household have not kept pace. Men do less housework than their counterparts in any other developed country, while women get less sleep than any of their counterparts, according to the OECD.

Government data indicates one way to turn the tide on the baby drought may be by divvying up domestic duties. The more time a husband spends on housework and child care on days off, the more likely his wife is to have another child, according to a welfare ministry survey.

Japan has been pushing for more fathers to take paternity leave to reduce the burden on families as its population declines and rapidly ages. Environment Minister Shinjiro Koizumi recently made headlines by becoming the first sitting Cabinet member to take paternity leave, following the birth of his son this month.

Koizumi will take two weeks of leave over three months, including shortened days and teleworking, a plan that has drawn praise for its progressivism, and some criticism. One Twitter user said in a widely liked post that “shorter days and telework are not child care leave.”