Two weeks ago, President Trump warned Russia to “get out of” Venezuela after two of Moscow’s military planes landed in Caracas, the Venezuelan capital, to unload supplies and military personnel. But Mr. Trump has done little else to publicly engage as the crisis continues.

That role has fallen to Mr. Pence. But on Wednesday, he did not give a firm answer when asked by a reporter where the United States would draw a line on Russia’s involvement. He also did not give a timeline when asked if the possibility of American military intervention, an option long played up by administration officials, was drawing closer as conditions in Venezuela worsened.

Instead, the Trump administration has tried to choke off Mr. Maduro’s economic resources. Last week, it announced a round of sanctions targeting oil shipments between Venezuela and Cuba, the latest in a string of initiatives meant to curb Caracas’s ability to do business. Visas have been revoked in recent weeks for hundreds of Mr. Maduro’s associates.

In briefings held before Mr. Pence arrived to speak, United Nations officials warned of a situation that has only grown more dire as unrest continues and said that offering relief to Venezuelan citizens should not be a political issue.

Mark Lowcock, an under secretary for humanitarian affairs, told the Security Council that a recent draft overview of the situation by the United Nations indicated that around 1.9 million people require nutritional assistance because of worsening food availability, including 1.3 million children under 5. Additionally, Mr. Lowcock said, tuberculosis, diphtheria, measles, malaria and other preventable diseases have resurfaced in Venezuela.

Food shortages also remain a main factor in driving people out of the country: Surveys show that 80 percent of Venezuelan households struggle with finding enough food, United Nations officials said.

“In Venezuela, there is a need to separate political and humanitarian objectives,” Mr. Lowcock said. “Humanitarian assistance must be delivered on the basis of need alone.”