Her first priority included increasing nurseries and day care for children, she said. Paternity leave came later. “My basic idea was that men and women should share rights and duties. The idea is that men should be real parents.”

Even with their increased clout, Swedish women still face many barriers, at work and at home. “Is the Last Mile the Longest” was the question posed in the title of a May 2018 report on “Economic Gains From Gender Equality in Nordic Countries,” by the O.E.C.D. The report concluded that while the Scandinavian countries have come closer than other countries to narrowing the gender gap, the challenge to closing it altogether remains stubbornly difficult.

In recent years, some have argued that Sweden’s reputation as the best in the class on gender equality has slipped. In 2007, Sweden ranked No. 1 on the World Economic Forum’s Global Gender Gap Report; now it is in third place. Many fathers still resist taking an equal share of the generous 480 days of parental leave provided at the birth of a child, leaving mothers to assume the greater responsibility for child care and house work, studies show. The wage gap between men and women is still there (women get 88 percent of men’s wages) and in 2016, only 6 percent of chief executive positions in listed companies where held by women and 5 percent of board chairmanships.

“We still have a lot to do,” said Ms. Lindhagen, who has set efforts to combat domestic violence and to increase women’s economic power as her top priorities as a member of Sweden’s new coalition government.

Sweden has resisted the move to legislate the kind of quotas for women in top corporate positions adopted in neighboring Norway in 2003, followed later by France, the Netherlands and Spain. Ms. Lindhagen said the emphasis still should be on improving working conditions so that women can thrive and be promoted. “Then if it isn’t happening, if it is taking too long, then I could say we should look at quotas,” she said.

Voluntary quotas for women candidates were adopted over the years by Sweden’s political parties, but according to Ms. Dahl, the important work was done before quotas. “First we laid the groundwork to facilitate women’s entry into politics,” she said in a 1998 report on women in politics by International IDEA, a Swedish foundation. “We prepared the women to ensure they were competent, and we prepared the system, which made it a little less shameful for the men to step aside.”

But numbers don’t tell the whole story. In France, where the president, Emmanuel Macron, in 2017 named a cabinet divided equally between men and women, journalists and other observers note that the top staff in the ministries, and in the presidency itself, are male dominated.