A vendor at her kiosk in this Ukrainian city 350 miles from Chernobyl greeted a request for local newspapers with a knowing look. "All sold out. Anyway, the best news about the nuclear accident is in the Kiev papers," she said, flipping the pages. "Here, read for yourself."

In Odessa, where Chernobyl is still the talk of the town, official assurance that the nuclear disaster is far away and under control belies a sense of public anxiety about the lingering effects of radiation.

Ukrainian officials here took Soviet leader Mikhail Gorbachev's speech on Wednesday as an assurance that the Chernobyl disaster was past. Taking a cue from him, in interviews about the incident they stressed the "anti-Soviet reaction" it provoked in the West, and the heroic efforts of Soviet rescue workers to deal with it.

Gorbachev indicated "the activity of our party and government to see that everything is being done for the sake of man," said Galina Izuvita, vice chairman of Odessa's City Council, in an interview the day after the televised speech. "He even looked concerned," she added.

Gorbachev made his first public comments about Chernobyl as concern about radiation appeared to peak in the Ukraine, and thousands of worried residents of Kiev -- 80 miles from the accident -- remained outside the city. Even after the speech, some residents here seemed unconvinced that health dangers resulting from the Chernobyl incident were resolved.

"Aren't you afraid to travel in this area?" a hotel worker asked a visitor, brushing aside assertions from Moscow that radiation emissions resulting from the April 26 nuclear power plant explosion stayed within safe levels outside the immediate area around Chernobyl.

A Soviet university student was more direct: "People here are saying that if you don't feel well, it must be the radiation."

A few days after the incident, winds swept increased radiation from Chernobyl through Kiev and southward, official Soviet reports said. Odessa, a city of 1 million, is 280 miles south of Kiev, on the Black Sea. Late last week, Soviet radiation readings in neighboring Moldavia were still above normal.

In Kiev, officials have reacted by recommending that people stay indoors, prohibiting the sale of food at sidewalk stalls, ordering children off the streets, and introducing other precautionary measures against the potential health hazards. But here, no radiation readings were given and no measures taken against potential radiation effects.

Local coverage of the incident, mostly culled from the national press, was at first subdued and later focused on appeals for financial assistance for evacuees and attacks on western coverage.

Children have played outside here since the accident was announced three weeks ago, and residents stroll around, eating ice cream and pastries from open-air vendors and dining in outdoor cafes.

Soviet, Finnish and East Bloc tourists are spending their spring holidays in resorts along the Black Sea. "There were rumors that there was a little radiation here," a taxi driver said, "but I don't know if there was or not."

In nearby Romania, officials expressed more alarm about the radiation from Chernobyl than did officials here. On May 2, when radiation crept across Romania -- whose border is 125 miles from here -- the Romanian official radio told people to stay indoors.

But the same day, the official Odessa newspaper, Znamya Kommunizma, carried two brief announcements about Chernobyl on its back page. On that holiday Friday, the sun came out here and temperatures rose to 72 . Residents bathed on the beaches and swam out into the chilly water.

"People are afraid and worried," said one woman, "but they won't do anything, of course. What would they do?"

Lacking official advice, one local student decided to take her own precautions. "I don't think I'll go out in the rain here for a long time," she said emphatically.

Asked his opinion of Gorbachev's speech, Nikolai Stofeev, a World War II veteran and local official, criticized U.S. arms control policies, attacked western exaggerations of the death toll and underlined Gorbachev's call to meet with Reagan.

Izuvita said she was impressed how Gorbachev talked "about those who suffered from the disaster and about what we, in the whole country, including Odessa, should do." Evacuated children will be spending their vacations in Odessa, she said, "so that their health will improve at the seaside."

A local Intourist guide, bristling at western warnings against using Soviet dairy products because they may have been affected by radiation, said: "We're still drinking milk here."