TOKYO — Japan’s revered emperor made his first trip Thursday to the disaster zone since the March 11 earthquake and tsunami destroyed much of the northeast coast and set off a crisis of radiation leaks at a flooded nuclear plant.

Emperor Akihito and Empress Michiko visited two evacuation shelters Thursday in Asahi city, about 86 kilometers (54 miles) east of Tokyo near the Pacific coast. The royal couple knelt on mats and spoke quietly with evacuees, who bowed deeply. Some wiped tears from their eyes.

Thirteen people died, and some 3,000 homes were damaged or destroyed in the city. The emperor and empress plan additional visits to other tsunami-affected areas in coming weeks. Overall, more than 26,000 people are believed to have died in the disaster, though only about 11,250 bodies have been recovered so far.

Nearly 140,000 people are still living in shelters after losing their homes or being advised to evacuate because of concerns about radiation leaking from the Fukushima Dai-ichi plant.

Although Japanese officials have insisted the situation at the crippled plant is improving, the crisis has dragged on, accompanied by a nearly nonstop series of mishaps and aftershocks of the 9.0-magnitude quake that have impeded work in clearing debris and restoring the plant’s disabled cooling systems.

The setbacks are angering and frustrating residents whose lives have been derailed by the crisis.

“I’m physically and mentally worn out,” said Yoshihisa Kato, a 66-year-old noodle shop owner in the town of Kawamata, which is about 28 miles (45 kilometers) northwest of the plant and in an area where officials have urged people to evacuate over radiation concerns.

“I’ve been going to funerals almost everyday because many elderly people in my neighborhood have died due to shocks and exhaustion,” said Kato, whose business has dried up as residents have fled the area.

Japan acknowledged this week that overall leaked radioactivity already has catapulted the crisis into the highest severity on an international scale, on a par with Chernobyl, though still involving only a tenth of the radioactivity emitted in that 1986 disaster.