Fears about the potential for a transborder nuclear disaster spread across Asia Tuesday as Japan's nuclear crisis deepened, even as experts and officials sought to calm fraying nerves in countries as far away as Singapore and the Philippines.

A policeman maintains order as people wait in line outside a store to buy Japanese milk powder in Hong Kong. Reuters

A series of explosions at the Fukushima Daiichi nuclear-power complex triggered a rush of concern across many countries in the region.

Memories of the nuclear disaster at Chernobyl, Ukraine, in 1986 were at the fore of many people's minds. After a reactor there went out of control during a test, an explosion and raging fire destroyed the reactor building, unleashing large amounts of radiation into the atmosphere. Radioactive material was blown over a wide area and traced as far north as Sweden and Finland before dissipating across the northern hemisphere.

Most experts say a repeat of the Chernobyl disaster is a distant prospect, largely because the reactors used in Japan are better designed and include a concrete and steel containment structure. The Fukushima plant was also shut down before a dangerous chain-reaction could develop. Yukiya Amano, the director-general of the United Nations' nuclear watchdog, the International Atomic Energy Agency, earlier described the probability of the current crisis morphing into a Chernobyl-like event as as "very unlikely".

Officials register radiation levels in Russia's Far East after Japan warned radiation levels had become "significantly" higher around the Fukushima Daiichi nuclear power plant, which has suffered serious problems in four of its six reactors since Friday's massive earthquake and tsunami. Video and image courtesy of Reuters.

But there is still much that scientists don't understand about the crisis in Japan, especially the question of how to best cool the reactors, and governments across the region began preparing for a possible escalation of the crisis by announcing plans to test food imports from Japan for signs of radiation.

Hong Kong, Singapore, Malaysia and South Korea were among countries saying they would monitor fresh produce for signs of contamination, while authorities in Thailand said they are ready to test all Japanese goods if necessary.

Staff from the Philippine Nuclear Research Institute monitor radiation levels in the air in Quezon City, Metro Manila on March 15. Reuters

Ordinary people in a range of countries also took preventive action. Residents in Russia's Far East bought up potassium iodide pills to prevent radiation sickness while military units based on the island of Sakhalin and the Kuril Islands just north of Japan prepared to evacuate if the nuclear threat worsens. "There has definitely been a run on these kinds of medicines in the last two days," said a salesperson at a pharmacy in Vladivostok.

In the Philippines, government agencies and medical organizations rushed to reassure Filipinos panicked by a wave of cellphone text messages which warned that a potentially deadly cloud of radiation was about to settle over the country. At the peak of the scare, Manila's Polytechnic University of the Philippines suspended classes after a deluge of calls from anxious students and parents. In a statement, university President Dante Guevarra said he shut the university, which is now open again, to help "eliminate any fear and stress."

The text messages were purportedly based on a news alert from the British Broadcasting Corp., and warned that people should "remain indoors first 24hrs" and "swab the neck" with an iodine solution because "radiation hits the thyroid first."

The BBC said it didn't issue any such message. A Philippines-based doctor, Mike Aragon, noted that even if radioactive particles drifted the 3,000 kilometers (1,864 miles) from Japan to Manila, applying iodine to a person's neck would offer "very limited protection, if any at all" from the effects of radiation, although potassium iodide pills can prevent the thyroid gland from absorbing radioactive iodine.

Among the many casualties from the Chernobyl meltdown, the International Atomic Energy Agency reports at least 1,800 documented cases of thyroid cancer in children under the age of 14. Radiation exposure can disrupt the body's natural control mechanisms and allow cancer cells to multiply.

Crucially, the Chernobyl plant lacked the concrete and steel containment structures used at Fukushima complex in Japan—something experts say is reducing the risk of a catastrophic, Chernobyl-style meltdown n Japan.

But the comparatively safer design of the Fukushima plan didn't stop the warnings from being quickly forwarded from cellphone to cellphone in the Philippines.

The barrage of text messages helped trigger a run on iodine-based products at many Manila drugstores, sales staff said, while doctors telephoned government hot lines to gauge the seriousness of the threat. Dr. Oscar Tinio, president of the Philippine Medical Association, said he telephoned government officials as soon as he got wind of the text messages, establishing that they were untrue. "It was a malicious hoax," he said.

Similar, often erroneous messages also appeared in Thailand and Indonesia, but the speed with which they spread in the Philippines prompted government officials there to launch a public-information campaign downplaying the scale of the threat.

In Thailand, Thai Airways International PCL said it would prevent its crew and cabin staff staying overnight in Japan to reduce the risk of employees being affected by radiation as worries about the extent of the nuclear threat deepened. Taiwan-based EVA Airways Corp. 2618.TW -0.63% EVA Airways Corp. Taiwan NT$15.65 -0.10 -0.63% April 21, 2014 1:12 pm Volume : 1.96M P/E Ratio 71.14 Market Cap NT$51.33 Billion Dividend Yield N/A Rev. per Employee N/A More quote details and news » , meanwhile, said Tuesday it will cancel 56 flights between Japan and Taiwan because of radiation concerns.

"I'm afraid the radiation could come to Thailand," said Sirima Patiphantakan, a 53-year-old shopkeeper in the northern Thai city of Chiang Mai. She said her family and neighbors were discussing what to do about the situation and, like people in the Philippines, had received cellphone messages about the potential danger. "We're trying to stay home as much as possible and keeping on top of the news," she said.

—William Mauldin in Moscow, Josephine Cuneta in Manila and Wilawan Watcharasakwet in Bangkok contributed to this article.

Write to James Hookway at james.hookway@wsj.com