(Measure passed Senate, amended) Anglo-Irish Agreement Support Act of 1986 - Earmarks specified amounts of the funds authorized for the Economic Support Fund for FY 1986, 1987, and 1988 for U.S. contributions to the International Fund (the Fund) established pursuant to the Anglo-Irish Agreement signed in November 1985. Authorizes using specified authorities contained in the Foreign Assistance Act of 1961 to support the Fund. Permits using such contributions only to support economic and social reconstruction and redevelopment in Ireland and Northern Ireland. Requires the President to make every effort to ensure that there is U.S. representation on the Board of the Fund. Authorizes the United States to make contributions to the Fund only if the President each fiscal year makes a specified certification to the Congress relating to the Board of the Fund and to the disbursements from the Fund. Requires the President to report annually to the Congress on the degree to which: (1) the Fund has contributed to reconciliation between the communities in Northern Ireland; (2) the U.S. contribution to the Fund is meeting its objectives; and (3) the Fund has increased respect for the freedoms of all people in Northern Ireland. Imposes certain requirements relating to funds for international organizations and conferences.