The presidential election in South Korea on Tuesday will be a big step toward stabilizing the country after months of political turbulence. But whoever wins — the left-wing front-runner Lee Jae-myung or his conservative rival Kim Moon-soo — will lead a nation in crisis.

South Korea’s economic growth has sputtered to a snail’s pace. Its income gap is wider than ever. Its suicide rates are among the highest, and its birthrates the lowest, in the world. Yet, the country has never been more politically divided — between the left and right, between generations and between young men and women. Whoever becomes the president will not be accepted by a large swath of the polarized society.

South Korea also faces formidable challenges from abroad. North Korea is threatening to use its expanding nuclear arsenal against South Korea. Russia has signed a mutual defense treaty with the North and is helping modernize its military. But President Trump has asked why the United States should spend so much money to keep its troops in South Korea. He has also slapped steep tariffs on cars, steel and other products that are crucial for South Korea’s export-driven economy.

South Korea needs to repair strained diplomatic ties with China, its largest trade partner, to help spur exports and economic growth. But the United States, its only military ally, is asking it to join efforts to contain China.

“A daunting and complex crisis is buffeting us,” said Mr. Lee, the Democratic Party candidate who is leading in the polls. “We must turn the crisis into opportunities.”