TOKYO — President Obama arrived here on Wednesday evening to begin a four-country tour of Asia, after first stopping in Washington State to survey the devastation left there by last month’s deadly mudslide. It was a fitting start, given that everywhere on this trip, he will witness the lingering fallout of disasters, natural and human-made.

From South Korea, where public outrage is surging in the wake of a ferry accident that has claimed the lives of scores of teenagers, to Malaysia, where the authorities face harsh scrutiny over their handling of a missing jetliner, Mr. Obama will encounter leaders under pressure from angry, often grief-stricken constituents.

In the Philippines, the government has labored to recover from withering criticism of its response to Typhoon Haiyan last fall. Even here in Japan, Prime Minister Shinzo Abe was tripped up by after effects of the 2011 Fukushima nuclear disaster and faulted last summer for playing down the leaking of highly radioactive water from the plant.

White House officials, who have come with a busy agenda of economic and security issues, worry that the leaders — particularly President Park Geun-hye of South Korea, for whom the ferry tragedy is still unfolding — will be preoccupied when they meet with Mr. Obama.