November 4, 1956
At 4:15 in the morning, Operation Whirlwind was launched with the explicit intent of crushing the revolution. Shortly after 5 AM a radio broadcast was aired with János Kádár announcing the new Hungarian Worker-Peasant Government. In it, Kádár announced that the revolution had devolved into a fascist uprising. The name of his new government was quite ironic, as many at the time noted, since the two largest social groups that had risen against communism were the workers and peasants.
In response to the Soviet invasion, Imre Nagy gave a speech on the radio in which he declared that the Soviets invaded to overthrow the legal and, quite importantly, democratic government. The speech was then replayed in a loop and read in various languages such as English and German.
Nagy and his associates took refuge in the Yugoslav Embassy, since although communist, Yugoslavia was not part of the Warsaw Pact. The intent was to not provide the Soviets with ammunition that he had turned into a western puppet. Cardinal József Mindszenty also took refuge, but he went to the American Embassy, where he remained until 1971.
Although in his post-invasion speech Nagy did not call for a renewal in armed resistance, the revolutionary groups nonetheless resumed the fight. As to why Nagy had not asked the revolutionary groups to engage in resistance, the general consensus is that Nagy knew it was hopeless and wished to prevent unnecessary bloodshed. In order to capture Budapest, the Soviets sent enough troops to occupy East Germany.
Although the fighting resumed, resistance would not be able to hold out forever. With the Soviet invasion, the 1956 Hungarian Revolution would come to an end.