The Soviet Union has asked Sweden about the possibility of sending patients suffering radiation burns from the nuclear power plant disaster at Chernobyl for treatment at Stockholm's famed Karolinska Institute, a well-placed Swedish source said today.

Soviet Ambassador Boris Pankin, who raised the issue during a meeting this morning with Jan Eliasson, head of the Swedish Foreign Ministry's political department, did not mention the number of cases involved, nor when they might be sent here, the source said. Sweden has agreed to give any assistance requested.

A Soviet statement issued in Moscow today said that 197 people had been hospitalized as a result of the nuclear accident. The statement said that 49 of them already had been released. Numerous unofficial and unconfirmed reports have estimated that casualties from the accident are significantly higher.

The Karolinska Institute, which is closely involved in the yearly selection of the Nobel prizes for medicine, has a sophisticated burn unit, although it does not necessarily specialize in radiation cases.

In a separate development, the director of Sweden's Radiation Protection Board said that the dose of radiation that the Swedish population has been exposed to is "of the same order as received by the affected people around Harrisburg," the Pennsylvania city nearest the Three Mile Island nuclear power reactor, where an accident occurred in 1979.

Although the area around the Three Mile Island plant was evacuated following the accident and the unit involved remains closed, no serious physical injuries or defects have been connected to radiation exposure there.

Sweden has been one of the countries outside the Soviet Union most seriously affected by the Chernobyl accident, which sent a radioactive cloud over Scandinavia during the weekend. The government here has been anxious to avoid panic and repeatedly has assured the Swedish population that it is in no danger. "We are, of course, a long way from lethal levels," said board director Gunnar Bengtsson at a news conference today.

But, Bengtsson said, officials here are particularly concerned about "unexpectedly high levels of cesium," an element contained in the wind-borne radioactive debris.

Rain and snowfalls have brought the radioactive debris to the ground in many parts of Sweden. "There are several very long-lived varieties of cesium, with half-lives on the order of years or even decades," Bengtsson said. "Up to one-fifth of the total activity covering the ground comes from this radioactive cesium. The other four-fifths will decay within a couple of weeks or so, so the radiation levels will go down."

But the cesium, he said, "will remain there, and go down very slowly . . . seeping down into the ground . . . [and] not decaying."

At the same time, measurements taken yesterday and last night have indicated "fairly high levels of radioactive iodine in still-standing water on the ground," Bengtsson said. The government here today issued recommendations warning people against using "nonrunning water," primarily from roof collection barrels or country ponds.

Radioactive iodine also has been found in mothers' milk and "milk that comes from farms," Bengtsson said, "but these levels are not sufficient to give any reason for concern." Measurements throughout the country indicate decreasing radiation levels in the southern part of Sweden to less than double the normal background radiation, with a similar decrease in the north. In the middle of the country, levels remain at about 10 times normal, Bengtsson said.

Although he said that northerly winds "for the next week or so" are expected to prevent any further radioactivity from the Chernobyl site from reaching Sweden, Bengtsson acknowledged that he did not "really trust weather forecasts too much."

"But if there was a change of wind direction," he said, "there would still be a traveling time of two days . . . to reach Sweden." Describing further significant fallout as "unlikely," Bengtsson said that the government nevertheless had made preparations that could include restrictions on the consumption of milk, which transmits radioactive iodine into the body, and "maybe asking people in some parts of Sweden to stay indoors."

Energy and Environment Minister Birgitta Dahl said in a broadcast interview today that "the catastrophe took place last Friday," although the Soviets made no official acknowledgement until Monday.

Yesterday morning, Sweden presented Moscow with a list of "specific, highly technical questions" about the nature of the accident and the current condition of the four-reactor Chernobyl site. But Foreign Ministry spokesman Ulf Hakansson said that Pankin, the Soviet ambassador, supplied no answers today in his meeting at the Foreign Ministry.

Pankin assured the Swedes that the Soviets had shut down the other three reactors at Chernobyl and said that "the risk of fallout is greatly reduced," Hakansson said. Swedish officials have said a fire in the graphite surrounding the reactor's nuclear fuel rods could burn for weeks.