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Ms. Park and the Obama administration likely will focus on maintaining the strong relationship that Mr. Obama shared with her predecessor, Lee Myung-bak, coordinating policy in response to North Korean provocations, implementing a free-trade agreement and revising a nuclear agreement, Mr. Cha said.

“They have a lot of issues on their plate,” he said. “But the U.S. feels confident in her capabilities.”

With the hawkish Shinzo Abe set to become Japan’s next prime minister, simmering territorial disputes between Japan and South Korea could prove explosive, creating a headache for Washington officials promoting a closer alliance between the two democracies as a buttress against rising China.

“We have two parallel leadership transitions and that circumstance carries with it both opportunity and risk,” Mr. Snyder said.

“[South Korea‘s] relationship with Japan is the one on which I see Madame Park is most constrained, primarily because the historical and territorial issues that have been sticking points in the relationship are ones that in Korea are associated to a certain extent with her father,” he added.

The South Korea-Japan relationship has been roiled by a dispute over a rocky outcrop of islands in the East Sea/Sea of Japan and the issue of comfort women used by the Japanese in World War II.

Ms. Park’s father was responsible for normalizing South Korea’s relationship with Japan and getting a Japanese loan that allowed South Korea to enter the steel industry and embark on the path to economic prosperity.

Miss Park will have to walk a very tight rope because of her father’s legacy,” Mr. Ku said.

Still, U.S. policymakers are likely relieved at Ms. Park’s victory: Mr. Moon had pledged to upgrade Seoul’s relations with Beijing, putting them on an equal footing with Washington, and renegotiate the Korea-U.S. free trade agreement.

Ashish Kumar Sen reported from Washington.