The Trump administration opened a double-barreled critique on Monday of what it described as a limp European response to the crisis in Venezuela, renewing demands for tougher sanctions against President Nicolás Maduro’s government and more aid for refugees.

The broadsides, delivered as leaders arrived for the annual United Nations General Assembly, sought to re-energize global support for Venezuelan opposition leaders who have been trying since January to oust Mr. Maduro from power.

Several European officials agreed that far more needed to be done to help the nearly seven million Venezuelans in desperate need of food, safe water and medical supplies. But they stopped far short of embracing any new sanctions against Mr. Maduro and his loyalists, including some who have assets in Europe.

The numbers of refugees fleeing Venezuela — expected to grow to five million by the end of 2019 — “are terrifying,” Edita Hrda, a European Union diplomat, told an Atlantic Council forum in New York. But she said attention to Venezuela largely has been limited to the Western Hemisphere, and noted that plans to broaden assistance would be a focus of a conference in Brussels in late October.