Ms. Park Geun Hye has eked out a victory in South Korea’s presidential election. The conservative candidate narrowly bested progressive rival Moon Jae In in a contest whose outcome was not apparent until the votes were counted.

Her win is an important moment for her country, not only because she is South Korea’s first female leader but also because of her pedigree — she is the daughter of assassinated dictator President Park Chung Hee. Her return to the Blue House marks a closing of the circle on her father’s reign.

The new president faces many challenges, and key among them is repairing relations with Japan.

Ms. Park has been a mainstay of South Korea’s conservative movement since before she even formally entered politics. Her father took power in a 1961 coup, and ruled South Korea with an iron hand while modernizing the country and laying the foundation for its rise to prominence as the world’s 14th-largest economy and an export powerhouse. He ruled for 18 years until he was shot to death by the head of his security force during a drinking party in October 1979.

Ms. Park took up the role as South Korea’s “first lady” following the death of her mother, who was killed in August 1974 during an assassination attempt on President Park, and served alongside her father until his own death five years later.

She continued her life in politics, taking her first seat in Parliament in 1998, representing her home town. The fact that she never married nor had children could have worked against her in a traditional society like that of South Korea, but she turned those facts around, using them to illustrate her devotion to the country as well as insulation against corruption, claiming that she has “no family to take care of and no children to pass wealth to.”

Perhaps most important for her Saenuri (New Frontier) Party is her election acumen. She has been an indefatigable campaigner in local and national elections, even staving off what looked like certain defeat for conservatives in National Assembly elections held earlier this year.

Her win ensures that conservatives maintain hold of the Blue House after current President Lee Myung Bak steps down in February after his mandatory single term.

This week’s ballot was close. Most polls had Ms. Park ahead, but her lead was always in the margin of error. When the final tally was concluded, she had bested Mr. Moon 52 percent to 48 percent. Voter turnout was the highest in 15 years, and while this was supposed to improve Mr. Moon’s chances, it proved insufficient.

It is not clear what Ms. Park will do with the presidency. She has said that she will promote “greater economic democratization,” which means that she will aim to ensure that the fruits of South Korea’s growth are more widely shared.

Income gaps are widening in South Korea and this has created great unease and social strains as the economy slows. South Korea’s economy is projected to expand just 2.4 percent this year, the slowest since 2009. While she will try to get that number higher, she is unlikely to tackle the chaebol, or family-owned conglomerates, that dominate the Korean economy.

Much too is expected of her as a woman, the first female leader of Korea since the ninth century. For all its economic success, South Korea has a dismal record promoting equality for women. It ranks 108th among the 135 countries of the World Economic Forum’s annual Global Gender Gap Report, and is 116th in economic participation and opportunity for women.

As in Japan, the poor choices afforded its increasingly well-educated women discourage them from marrying and having children. Yet observers note that Ms. Park has shown little interest in or attention to women’s issues throughout her career. Moreover, some critics wonder whether Ms. Park truly understands the problems faced by many women given her devotion to politics.

Two issues top her foreign policy agenda. The first is the perennial challenge of North Korea. The North has hewed to its hardline against Mr. Lee, and Ms. Park is expected to try to engage Pyongyang without abandoning her predecessor’s basic conservative principles.

Ms. Park met former North Korean leader Kim Jong Il in 2002, and found him to be someone “who would keep his word.” She is eager to resume dialogue with the North but not without conditions: She wants Pyongyang to give up its nuclear weapons plan as a pre-condition for economic aid.

For its part, the North has already charged Ms. Park with “kicking up hysteria for confrontation.”

The second issue is relations with Japan. There were high hopes that Mr. Lee would try to move relations with Tokyo to a higher level. Sadly after several missteps, the relationship plunged to new lows. We hope that Ms. Lee will use the opportunity afforded by the launch of a new government in Tokyo to try to restore a floor to the troubled relationship.

We urge Japan’s next prime minister, Mr. Shinzo Abe, to do his utmost to meet her more than halfway.

The greatest opportunity afforded Ms. Park is the chance to bridge the profound ideological divide that marks South Korea. Her father was a deeply divisive figure, a man who dragged South Korea out of poverty but who also imprisoned, tortured and executed his opponents. Indeed, Mr. Moon was one of those victims.

During the campaign, Ms. Park publicly acknowledged the excesses of her father’s regime and apologized to the families of its victims. Her willingness to openly address sensitive issues should serve her well in building a better relationship with Japan.

We wish her luck in all her endeavors.

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