The Soviet government tonight reported that radiation levels in Kiev were "somewhat higher" than normal, as signs accumulated of rising concern in that Ukranian city and other areas outside the original 18-mile danger zone.

The statement on Kiev's radiation, issued by the news agency Tass and read on the evening television news, quoted the Ukrainian health minister, Anatoly Romanenko, as saying it posed no health risks.

The government said radiation levels near the nuclear station, where a serious accident occurred, last month had "substantially decreased" and that the cleanup around Chernobyl was "nearing completion."

The latest government statement, provided along with a spate of press reports from the area, came as residents of Kiev, 60 miles south of Chernobyl, called relatives in Moscow to report new anxiety in the city, although foreign visitors said there was little evidence of panic.

A crowd was reported at Kiev's train station in the morning, and plane and train tickets out of the city reportedly were difficult to get. But the Soviet Union is in the middle of the holiday period between May 1, socialist Labor Day, and May 9, Victory Day, which could explain the rush of travelers.

A Canadian diplomat in Kiev told his embassy today that "reports of panic in the streeets were grossly exaggerated," one western diplomat said.

However, the lack of news in Kiev, the Soviet Union's third largest city, with a population of 2.4 million, apparently has created an undercurrent of unease among residents. Foreigners were stopped in the street and asked for information, milk was scarce in some neighborhoods, and radiation checks were being made available to Soviet citizens and foreigners, according to reports reaching Moscow.

Apparently in response to these accounts, Tass reported late tonight that although life is normal in Kiev, "of course there is also anxiety. Especially parents are concerned about their children."

Summer holidays are near, and lines have appeared at ticket offices, Tass confirmed. The agency said extra trains and planes are being added.

Tass also quoted Romanenko as saying on local television that people in Kiev did not need to take "preventive medicines" to counteract effects of the radiation. "All questions connected with the influence of the environment on the population's health are kept under unflagging control," he said.

Soviet scientists are uncertain, but believe that the hot nuclear fuel core in the Chernobyl reactor may have melted down through the floor and possibly even broken through the bottom of the plant into the earth underneath, according to a report on National Public Radio Wednesday.

The report cited a West German nuclear expert who has been consulting with the Soviet second secretary in Bonn on how to handle problems connected with the accident. The German expert said the Soviet diplomat in previous days had asked for advice on how to fight a graphite fire. But now, the diplomat has come back with questions about what happens if the core melts through the concrete floor of the building, and how quickly the radioactive uranium can contaminate ground water.

Hermann Rininsland, of the West German Nuclear Research Center, said, "The reason for all these questions was that they fear that there is a molten core or partially molten core that has . . . gone through the basement," NPR reported. Rininsland said, "We all believe it; I believe it, too. This molten material has penetrated this basement."

A Kiev Communist Party official today was quoted as saying that all vegetables for sale in the shops are checked twice, once in the field and once in the shops.

Soviet newspapers, which for 10 days carried only terse government announcements on the accident, today, for the second day, carried stories providing more details on the accident, the evacuation and life in the area.

Most accounts said the major evacuation effort began April 27, a day after the accident, involved 1,100 buses and lasted less than three hours.

In an interview with Tass correspondents carried in the newspaper Sovietskaya Rossiya, Grigory Revenko, first secretary of the Kiev regional Communist Party committee, said the most difficult task had been to persuade rural people to leave their homes.

"Many peasants did not want to abandon their homes,"Revenko said. "But we could not risk their lives, or their health. Therefore, in many cases, we had to persuade them."

Revenko praised people now working at the nuclear power station, said by Soviet officials at a press conference yesterday to number 150.

But Revenko said, "We cannot only supply optimistic information. One cannot hide a sin: There were particular workers who in difficult conditions did not display the necessary steadfastness or readiness to be at the front line."

Revenko's criticism of the initial response to the accident followed comments made in Moscow yesterday by Boris Shcherbina, deputy prime minister and head of a government investigating commission, who said Moscow had not been given a full picture of the situation by local officials.

Some confusion has arisen over the date of the main evacuation from Pripyat and three other towns surrounding the power plant. Yesterday, the Communist Party newspaper Pravda, the first to provide details of the accident at Chernobyl, indicated that the evacuation took place Saturday, April 26. Officials at a press conference yesterday said it took place on Sunday, the 27th.

A Tass account today said the evacuation in Pripyat, the town of 25,000 that lies closest to the nuclear plant, took place "immediately after the accident."

But in Izvestia, the government newspaper, a detailed account of the evacuation efforts said that planning began on the 26th when republic officials began to arrive.