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With his unanimous re-appointment for a second five-year term, the position of the Secretary-General had been strengthened both from a political and a constitutional point of view. 

In several speeches and press conferences, Dag Hammarskjöld supported the values of private diplomacy in peacemaking. On 5 February, he delivered a speech at Ohio University, The Element of Privacy in Peacemaking, where he urged greater recourse to quiet diplomacy in the work of the United Nations. He also discussed the role of the media in reporting world events:
 

"The media of mass communications, when supplemented by education in world affairs in schools and universities, provide powerful tools for developing a better informed public opinion. However, they can also be misused. We learned between the First and Second World Wars that public diplomacy could not in itself provide insurance of peace, for in the hands of a ruthless group of rulers the mass media has been misused to build strong public support for the wildest aspirations of these rulers and thus to place an additional weapon in the hands of those who wanted to lead the world in the direction of war, not peace. Thus the mass media can be misused under certain circumstances for harmful propaganda. Where competitive conditions prevail there is also a tendency to play up conflict because conflict usually seems more dramatic than agreement. For the same competitive reasons there is also the natural desire to be "first with the story". In international affairs, this may result in premature and often poorly informed publicity about an issue at a time when the privacy of quiet diplomacy is essential to achieving a constructive result. At the same time I recognize that public opinion cannot be truly well informed about the progress of peacemaking unless it understands the part that is played at all stages by private diplomacy and its relationship to the public proceedings of parliamentary diplomacy which are so fully reported. This creates difficulties both for the private negotiator and the representatives of the mass media..."

On 10 April, Dag Hammarskjöld started his second term of office. In an address to the staff, he quoted a Swedish song that culminates in the words: "Will the day ever come when joy is great and sorrow is small?" and went on to say: 
 

Looking at it in terms of humanity, looking at it in terms of the development of human society, it can be said, of course, that what we are trying to do here is to make our small contribution, during our short time, to a development which will finally lead us to the day "when joy is great and sorrow is small." However, you can also look at those words in a much more personal and intimate sense. I think it is possible to interpret them superficially but it is also possible to interpret them in a sense which goes to the very heart of our way of settling our relation to life. And then I would say that, on the day we feel that we are living with a duty, well fulfilled and worth our while, on that day joy is great and we can look on sorrow as being small."

On 27 May, the Security Council included the Lebanese complaint in its agenda but postponed further consideration of the item until 3 June, as the League of Arab States was to consider the matter on 31 May. After a further postponement, in order to permit the Arab League to complete its consideration of the matter, the Security Council began its discussion on 6 June. 

The majority of Security Council members expressed their concern at what was termed the grave situation described by the Lebanese representative. On 11 June the Security Council adopted a resolution (S/4023) [ Chinese|French| Russian], submitted by the representative of Sweden, whereby the Council decided "to dispatch urgently an observation group to proceed to Lebanon so as to ensure that there was no illegal infiltration of personnel or supply of arms or other matériel across the Lebanese borders" and authorized the Secretary-General to take the necessary steps to that end. The was thus created. 

Until 9 December, when the United Nations Observation Group in Lebanon officially ceased its operations, due to the re-establishement of cordial and close relations between Lebanon and the United Arab Republic, the Observation Group continued to develop its activities pursuant to the Council resolution of 11 June. 

The Second United Nations International Conference on the Peaceful Uses of Atomic Energy was held in Geneva from 1 to 13 September. Preparations for the Conference had been made over the previous two years, under Dag Hammarskjöld's direction and with the expert assistance of the United Nations Advisory Committee on the Peaceful Uses of Atomic Energy. The Conference brought 2,700 delegates and advisers from 69 countries together to review the uses of nuclear energy and to consider how it might be used most fruitfully in the future. Over 4,600 abstracts and scientific papers were submitted. 

On 16 October, the Secretary-General presented a report on the Conference to the General Assembly, and stated that the conference gave "a synoptic presentation of a vast and complicated area of science and technology and thereby opened the door to a fruitful exchange of knowledge and ideas among specialists in numerous scientific disciplines from many nations". The report also included recommendations for the future, and a resolution was adopted by the General Assembly based on this report. The resolution continued the Advisory Committee with the same membership but with the broader title of the United Nations Scientific Advisory Committee, and provided that "henceforth it shall advise and assist the Secretary-General, at his request, on all matters relating to the peaceful uses of atomic energy with which the United Nations may be concerned."

On October 9, Dag Hammarskjöld submitted to the General Assembly a . He wanted to put on record his conclusions on this pioneering experiment in international affairs, and to encourage governments in their own study and evaluation of these conclusions.

After two years of trying, Dag Hammarskjöld finally secured acceptance by the General Assembly of his proposal for an international administrative service to supplement the technical assistance programme. On 14 November, the General Assembly adopted five resolutions [ Chinese|French| Russian| Spanish ] that continued and developed the Expanded Programme by providing operational or executive assistance to governments. Dag Hammarskjöld described such assistance as being: "the complete antithesis of anything in the nature of a colonial arrangement."

In December, the Secretary-General travelled to the Middle East and Africa. He spent Christmas with the United Nations Emergency Force, visiting both Gaza and Sharm el Sheikh. He had talks in Cairo and Jerusalem. On 29 December, he was in Addis Ababa, Ethiopia, to attend the opening of the first session of the Economic Commission for Africa (ECA). ECA had been established during the 1958 spring session of the Economic and Social Council as the fourth regional economic commission of the United Nations. The Council had also decided that Addis Ababa would be the seat of the Commission.