Both the Soviet Union and the US used radio to communicate directly with each other, complementing the more traditional diplomatic channels. To seek a resolution to the crisis, the Soviet leader, Nikolai Khrushchev, used Radio Moscow knowing that his words would be monitored and reported long before the official communiques reached the Oval Office, and in the circumstances time was certainly of the essence. Khrushchev's first letter to President Kennedy on 26 October 1962 had been subject to a long delay in its transmission to Washington from the US embassy in Moscow. This was a gamble the Soviet leaders were no longer prepared to take, hence radio was considered the fastest method of communicating with the American President. On 27 October the US issued a statement welcoming Khrushchev's communication to remove the missiles in Cuba in response for a promise that there would be no US invasion of the island. This statement ignored a second message, broadcast twice on Radio Moscow, demanding the US remove its missiles from Turkey in return for a climbdown in Cuba.
At 1405 GMT (0900 Washington time) on 28 October 1962, Radio Moscow announced that it would transmit an important government statement, the broadcast beginning even before its textual editing had been completed. No clearer warning could be issued to the BBC's monitors at Caversham Park that they should prepare to receive, transcribe and report what followed.
As in previous broadcasts, Khrushchev addressed Kennedy personally as 'esteemed Mr President', informing him that 'the Soviet government, in addition to orders previously issued for the cessation of further work on the [Cuban] building sites for the weapons,' had 'issued a new order; for the weapons which you describe as "offensive" to be dismantled, packed up and returned to the Soviet Union.'
The significance of this broadcast, and the importance attached to it by the Soviet leadership's insistence that it be monitored and reported, can be adduced by the fact that it was repeated four times in the home service and no less than thirteen times in the North American service, in addition to several repeats in Spanish for listeners in Cuba.
Kennedy decided to accept the terms of the message in the same way that he had received it - over the radio. James A. Nathan has described this as a 'considerable departure from diplomacy'.  But there was nothing diplomatic about this particular communication. It was not an act of negotiation or the basis for further discussion, but was rather a public announcement of intention which, by its very nature, lacked flexibility and the capacity for compromise.
Kennedy's welcome of Khrushchev's decision was duly reported by TASS and in Moscow Radio's home service on 28 October, though it was not published in Russian newspapers until 30 October, a delay designed to strengthen Khrushchev's image as a hero who had taken a firm stand to avert war. Radio Moscow told its listeners in North America that the Soviet government's decision to end the crisis should not be regarded as a sign of weakness. On the contrary, the country had 'displayed forbearance ... in an effort to keep world peace. It did a service to all of humanity with a courageous restraint and refusal to be provoked, for it saved the world from thermonuclear disaster. ... Only a country confident of its strength could take the stand the USSR has taken'. 
Kennedy said he felt 'like a new man. Do you realise,' he asked his friend, Dave Powers, 'that we had an airstrike [against Cuba] all arranged for Tuesday [just two days later]? Thank God it's all over'. 
 Nathan, James A. (1988), 'Cold War Model' in Robert A. Divine (ed.) The Cuban Missile Crisis (New York: Markus Wiener) p.342
 BBC Summary of World Broadcasts, Part I, 31 October 1962.
 Quoted in Beschloss, Michael R. (1991), Kennedy v. Khrushchev: The Crisis Years, 1960-1963 (London: Faber & Faber), pp.541-2