BANGKOK—The Thai capital became two different cities Sunday: one where some relieved residents saw river embankments mostly withstand weekend peak tides, and another where refugees continued to flee a Kuwait-sized, polluted mass of water slowly bearing down on the north of the city.

In one moment fraught with symbolism, Prime Minister Yingluck Shinawatra's government was forced to abandon its own flood-crisis center at Bangkok's old international airport on Saturday as the deluge there worsened, setting up a new hub at the...