SEOUL, South Korea — The coronavirus spread to more countries and the numbers of new cases and deaths outside of China climbed, with special concern focused on South Korea, where infections doubled in a single day — raising fears that another Asian country was losing control of the escalating epidemic.

By Saturday, the virus had been identified in two new countries, Lebanon and Israel, bringing the spread to 28 countries, with about 1,500 confirmed cases outside of China, where it originated. The death toll in Iran rose to six, the highest outside of China, and the number of confirmed cases there reached 28, though experts suggest that the real number is likely to be far higher.

South Korea’s prime minister, Chung Sye-kyun, called the situation in his country “grave” and urged citizens to cooperate with the government and avoid large political gatherings, which have continued in the capital, Seoul, despite a city ban.

“The government will sternly deal with acts that interfere with quarantine efforts, illegal hoarding of hygiene goods and acts that spark uneasiness through massive rallies,” Mr. Chung warned in a nationally televised address.