As rescue crews worked into the night under the powerful are lamps and the gaze of the curious, the official news agency said that more than 300 bodies are recovered here in Romania's capital since Friday night's earthquake.

Radio Bucharest said that at least 370 persons had been killed and nearly 2,400 injured. In the first official casualty figures released, the radio said the known death toll so far was 298 in Bucharest and 72 in other parts of the country. It said 1,773 were injured in the capital - 1,200 of them seriously.

Western diplomats calculated, however, that at least 2,000 and perhaps as many as 3,000 people died in Bucharest alone. They based their estimate on American medical students helping in hospitals. Diplomats quoted Romanian officials as saying privately that the quake - which shook all of eastern Europe - had killed at least a thousands Romanians.

[Soviet officials said the tremor was feit in Moscow but caused no damage there, and Moscow television said the quake was felt in Leningrad and Sochi, on the Black Sea. Saturday night Moscow television showed film of damage the shock had inflicted in the Soviet Republic of Moldavia, but said there had been no deaths or injured, the Associated Press reported.]

In Bulgaria, an early official report said 20 persons had been killed, 165 injured and 60 buildings destroyed. Yugoslavia reported 17 injured, the Associated Press reported.

[Other Associated Press reports quoted officials in Greece as saying five separate tremors were felt and that they caused a brief panic in the northern city of Salonika. In Italy, government spokesmen told the news agency the tremors caused tall buildings to sway in Rome, Naples, and most of the central part of the country.]

While most of the destruction and loss of life were caused by the collapse of large apartment blocks in the capital, Bucharest radio tonight said that other parts of Romania had also been seriously affected.

The radio mentioned Craiova, some 120 miles west of Bucharest, where the university and city center have been largely destroyed. So far there are no detailed casaulty figures from the city.

President Nicolae Ceausescu cut short an African tour to take personal charge of the relief work in Bucharest. He declared a state of national emergency and visited the most seriously affected areas in the city center.

Offers of aid and relief poured in from abroad, including a promise of U.S. support. U.S. Embassay officials said that the Romanian Foreign Ministry had not yet responded on the offer.

Amercian diplomats said that as far as is known no American citizens have been killed or injured but a large number of embassy personnel have had to move out of their homes for safety reasons.

The extent of the damage in Bucharest was not immediately apparent to people driving into the city. In the suburbs, where damage was relatively slight, almost a holiday atmosphere prevailed, with large crowds out in the streets and most shops shut.

The real horror was in the central commercial area, where once-mighty apartment buildings looked like pieces of crumbled cheese. Soldiers brought into the capital kept the crowds at bay good humoredly, but a smell of building rubble was in the air.

All semblance of traffic regulations appear to have been put in abeyance - with policemen turning a blind eye to illegal U-turns or to driving the wrong way down one-way streets.

Crowds watched as rescue workers using heavy equipment dug into the rubble that had been Bucharest's fashionable Dunarea restaurant. The restaurant, which would have been at its busiest when the quake struck at 9:30 in the evening, occupied the ground floor of a nine-story apartment building.

The building had collapsed "like an accordion," one floor upon another, according to a witness.At least a dozen highrise apartments in the city were leveled by the quake.

Government officials say their major aim is to provide shelter for the thousands of people believed to have been made homeless by the earth-quake. Some have already gone to stay with relatives.

Roads leading to Bucharest from the provinces are thronged with hitch-hikers desperate to get a lift to the capital to see what has become of their families.