The collection "Speeches" of the UN Digital Library allows searching by name of speaker and by country name.
In addition, if the speaker is head of state or government, the title of the office (president, prime minister, queen, etc.) is included in the country/organization field.
For example, to search for statements made by the presidents of France, enter the terms into the search box and click on Search.
This will return results of all statements made in meetings of the Security Council starting in 1964, the General Assembly and Economic and Social Council starting in 1983, and the Trusteeship Council starting in 1982.
Ask DAG has an entry for the General Debate statements of each Member State. The entries include the link to meeting records and the name of the speaker.
In addition, an older document, entitled "List of Speeches and Visits Made by Heads of State and Dignitaries", covers the years 1946-1976 (ST/OGS/SER.F/4 + Add.1 + Add.2).
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