The optimists among them are expressing relief that Donald J. Trump said nothing during the campaign about dismantling the United Nations altogether — or turning its iconic tower facing the East River into condos.

Those who represent the United States' closest allies are trying to learn who Mr. Trump will appoint to crucial foreign policy jobs and how he will actually approach the pressing crises that are sure to come up before the Security Council: Syria, Ukraine, North Korea and the widening chasm between the Israelis and the Palestinians. Not least, many are trying to persuade his transition team to respect the international deals the United States has accepted under the auspices of the United Nations.