TOKYO— Yumi Suzuki is an anomaly in Japan’s male-dominated world of construction. She was one of six women studying architecture in the ’70s in college, among a class of 100 male students. Superstition about the jealous goddess of the mountains prohibited women from entering tunnels during construction. Her employer,Taisei Corp. 1801.TO -0.34% , kept its female employees in assistive positions when she began working there in 1981.

A quarter century later, Ms. Suzuki is a general manager at one of the country’s largest construction firms, overseeing a team of about 20—making her one of its two senior female managers. Taisei, with 13,600 employees, recently adopted a goal to triple the number of female managers by 2020. “It would be good to give an extra boost to help women,” says Ms. Suzuki, a 55-year-old architect.

With its aging population and dwindling workforce, Japan more than ever is looking to women like Ms. Suzuki. Prime Minister Shinzo Abe has brought the issue to the forefront of his economic-growth policy known as “Abenomics,” proclaiming a goal to fill 30% of leadership positions in Japan with women by 2020. On Friday, Mr. Abe is hosting a forum called “Women’s Power as the Source of Growth.” Among the guests are Christine Lagarde, managing director the International Monetary Fund, and Caroline Kennedy, Washington’s ambassador to Tokyo.

According to government figures, only one in 10 managers in Japan are women, compared with 31% in Singapore, 38% in Germany and 43% in the U.S. To demonstrate the need for change, Mr. Abe himself appointed five women as ministers to his new cabinet last week—increasing the female representation to 26% from 10%.

“I believe that the hard work of the women in the cabinet will bring on social change,” Mr. Abe said after the reshuffle.

Business leaders and women themselves, however, question the effectiveness of gender-based numerical targets.

With just six years to go, some say Mr. Abe’s goal is unattainable and worry that a focus on personnel statistics could divert attention away from essential but time-consuming changes needed to keep women in the workplace. “It’s about work-life balance, worker productivity, training female employees, diversifying work styles—issues that companies have been trying to address for about 20 years,” says Yoko Yajima, a diversity consultant at Mitsubishi UFJ Research and Consulting.

Japan Inc.’s notorious long work hours is blamed for hurting its productivity and global competitiveness while shrinking the pool for potential female managers by forcing many to give up full-time employment after childbirth.

Prime Minister Shinzo Abe is trying to get more women into managerial positions as part of his economic-growth policy known as “Abenomics.” Bloomberg News

“The motive behind raising the number of women managers should be about easing access to opportunities and diversifying the way they work. Not sticking as many women as they can find into senior positions,” says Akiko Kojima, an analyst at Japan Research Institute who specializes in corporate gender issues.

Keidanren, Japan’s powerful business lobby, was initially reluctant to respond to Mr. Abe’s call—the group itself is a male-dominated organization, with zero female presence in its 24-member board. But in July, it called upon its member companies to publicize their gender equity strategy. Taisei, the construction company where Ms. Suzuki is a manager, was among about 50 companies to do so. Still, its modest goal to triple the number of female managers will barely make a blip. Given the structure of the company, Mr. Abe’s 30% goal is just not feasible in such a short time, said Tetsuya Shioiri, Taisei’s personnel diversity manager.

Gender quotas are a divisive issue even in Europe where female executives and political leaders are increasingly becoming the norm. A European Parliament proposal to require publicly listed companies to have at least 40% female nonexecutive board members by 2020 is awaiting approval among European Union states—and not without debate. A recent study published by the National Bureau of Economic Research reviewing a similar law passed in 2003 in Norway showed it had “very little discernible impact on women in business beyond its direct effect on the newly appointed female board members.”

“I was strongly against [quotas] because I thought women should be recognized on their own merits,” said the IMF’s Ms. Lagarde, in January at a panel discussion in this year’s World Economic Forum. Ms. Lagarde says she’s now “pro-quota, pro-targets” after seeing how few women made partners at a law firm where she worked.

Advocates say women could benefit more from quotas in Japan, where gender equality is nowhere near European levels and traditions and convention dictate work practices. “If it’s a question of chicken or the egg—perhaps having adult chickens for show, to advertise to young women that they too can be leaders will lead to more eggs,” says Ms. Suzuki, the architect.

Write to Toko Sekiguchi at toko.sekiguchi@wsj.com