GENEVA — Delivering a stiff rebuke to the Trump administration over its handling of migration issues, the International Organization for Migration rejected on Friday the American president’s choice to become the agency’s next executive director, choosing instead a former deputy prime minister of Portugal.

The election of the new leader, António Vitorino, was seen as a barometer of United States influence in multilateral agencies after President Trump’s decision to withdraw the country from international commitments on climate and trade, as well as from the United Nations Human Rights Council.

“This reflects the reaction to the overall Trump approach to international organizations, the United Nations, and its decision to withdraw from the Human Rights Council,” Ted Piccone, a senior fellow at the Brookings Institution, said by telephone from Washington. “There’s a clear pushback against the Trump agenda.”

Mr. Vitorino was approved after the American candidate, Ken Isaacs, was forced to withdraw after finishing last in three rounds of early voting. The result was confirmed by Leonard Doyle, the communications director for the immigration agency.