SEOUL, South Korea (AP) — The country with the developed world's biggest gender income gap now has its first female president, but Park Geun-hye already has South Koreans wondering whether she'll improve the status of women in a society still dominated by men.

Wearing a traditional Korean dress of red and gold silk, Park strode up the steps of the presidential Blue House after her inauguration Monday. So far, she has chosen only two women to join her in top positions — two less than a male liberal predecessor.

Park faces expectations that she will do something about pervasive sexism, and many other issues. Those include authoritarian rival North Korea, which conducted a nuclear test two weeks ago and warned Monday of a fiery death for Seoul and its ally Washington.

South Korea also struggles with deep societal rifts that many trace back to the 18-year dictatorship of Park's father. With a stagnant economy and job worries, there's pressure for Park, a member of the conservative ruling party, to live up to campaign vows to return to the strong economic growth her father oversaw — the so-called Miracle on the Han River.

Park's election in December was an important moment for women in South Korea, who on average earn nearly 40 percent less than men, the largest gap among the 26 member nations of the Organization of Economic Co-operation and Development. South Korean women are often paid less for doing the same work as men and seldom rise to the top of high-profile industries.

During her presidential campaign, Park criticized "traditionally male-centered politics" for corruption and power struggles, saying that "South Korean society accepting a female president could be the start of a big change."

Critics, however, are taking note that Park has nominated women for only two of 18 Cabinet posts — and that one of those positions, the minister responsible for gender equality, hasn't been held by a man since being launched in 2001. Park's conservative predecessor, Lee Myung-bak, also nominated two women to start his term, while former President Roh Moo-hyun, Lee's liberal predecessor, named four.

Kyunghyang Shinmun, a liberal daily newspaper, pointed out in a recent editorial that there are no women among the 12 officials tapped as senior presidential advisers.

Park's nomination of so few women is disappointing, as there was a high public expectation for better gender equality in her Cabinet, said Park Seon-young, a researcher at the government-affiliated Korean Women's Development Institute in Seoul.

Park either didn't search hard enough for qualified women for her Cabinet, the researcher said, or such women were filtered out during a screening process.

Park's inauguration was attended by at least one other female world leader, Thai Prime Minister Yingluck Shinawatra. U.S. National Security Adviser Tom Donilon and Japanese Deputy Prime Minister Taro Aso also attended.

Before Park took her oath of office, South Korean superstar PSY performed his global hit "Gangnam Style" before tens of thousands. Children and the elderly alike joined him in the contagious horse-riding dance he made famous in the song's video.

In her inauguration speech, Park mentioned North Korea's Feb. 12 nuclear test, its third since 2006, calling it "a challenge to the survival and future of the Korean people" and saying Pyongyang should abandon its nuclear ambitions and work for peace.

"There should be no mistake that the biggest victim will be none other than North Korea itself," she said.

As Park was sworn in, North Korea's state media, referring to the North as a "full-fledged nuclear weapons state," criticized Seoul and Washington over annual military drills that Pyongyang calls an invasion rehearsal, warning that the allies would "die in flames" if they attack.

North Korea's nuclear test sets up a challenge to Park's vow to soften Seoul's current hard-line approach to Pyongyang.

Pyongyang, Washington, Beijing and Tokyo are all watching to see if Park pursues an ambitious engagement policy meant to ease five years of animosity on the divided peninsula, or if she sticks with the tough stance of former President Lee Myung-bak.

Park's decision will likely set the tone of the larger diplomatic approach that Washington and others take in stalled efforts to persuade North Korea to give up its pursuit of nuclear weapons.

"If Park Geun-hye wants to contain, the U.S. will support that," said Victor Cha, a former senior Asia adviser to President George W. Bush. "But if Park Geun-hye, months down the road, wants to engage, then the U.S. will go along with that too."

Park's last stint in the presidential Blue House was bookended by tragedy: At 22, she cut short her studies in Paris to return to Seoul and act as President Park Chung-hee's first lady after an assassin targeting her father instead killed her mother; she left five years later, in 1979, after her father was shot and killed by his spy chief during a drinking party.

Her first weeks in office will be complicated by North Korea's warning of unspecified "second and third measures of greater intensity," a threat that comes as Washington and others push for tightened U.N. sanctions as punishment for the nuclear test.

That test is seen as another step toward North Korea's goal of building a bomb small enough to be mounted on a missile that can hit the United States. Pyongyang called the test a response to U.S. hostility.

Park has said she won't yet change her policy, which was built with the high probability of provocations from Pyongyang in mind. But some aren't sure if engagement can work.

The economic aid and other benefits that North Korea would have received by "choosing electricity over bombs ... will be made much more difficult, if not impossible, for at least the next five years," American scientist Siegfried Hecker, a regular visitor to North Korea, said in a posting on the website of Stanford University's Center for International Security and Cooperation.

As she takes office, however, Park will be mindful that many South Koreans are frustrated at the state of inter-Korean relations after the Lee government's five-year rule, which saw the North conduct two nuclear tests and three long-range rocket launches. In addition, attacks blamed on North Korea that killed 50 South Koreans in 2010.

So far, Park's transition to power has been rocky.

She began her first day as president with lawmakers deadlocked over her government restructuring plans, which include newly created or revamped ministries. Some of the people she has nominated for ministry posts have been accused of tax evasion, real estate speculation and ethical lapses.

Park handed top jobs to people with ties to her father, reviving claims in the campaign that she doesn't fully understand her father's complicated legacy. Park Chung-hee is both reviled as a dictator and human-rights abuser, and revered for leading South Korea from the economic rubble of the Korean War.

To help an economy facing weak overseas demand for South Korean products and record household debt that's hurting domestic demand, Park plans to spend more than two thirds of the annual budget during the first half of the year, and announced an 18 trillion won ($16.6 billion) fund meant to aid debt-burdened South Koreans.

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AP business writer Youkyung Lee contributed to this report.