One American stuck in the South American nation said he received similar information from the office of Sen. Diane Feinstein (D-Calif.), the top Democrat on the Intelligence Committee. Feinstein’s office did not respond to a request for comment.

“[The State Department’s] planned repatriation flights have not yet been approved by the Peruvian government,” read an email from Feinstein’s office to the stranded Americans. “They are requesting reciprocal support for their own citizens to leave the United States.”

The State Department said it flew a group of Americans home on Saturday, including “medically vulnerable” citizens and some Peace Corps volunteers and embassy personnel. But a spokesperson did not comment on whether the Peruvian government is preventing the rest from leaving. U.S. diplomats estimate a few thousand Americans remain in Peru, a spokesperson did not respond to a question about the number.

Peruvian officials, meanwhile, say they are merely trying to figure out how best to get each nation’s residents home.

"We are actively engaging State Department officials to coordinate in a harmonic way the best way to carry out bringing Americans from Peru back to the U.S. and Peruvians in the U.S. back to Peru," said Rodolfo Pereira, press counselor for the Peruvian Embassy in Washington. "What we are trying to set up is the best system to conduct that operation."

Pereira dismissed questions about tensions between the two sides, saying there are constant communications, including at high levels, and that much of what is being discussed is logistics.

In a phone interview, he said he didn't know exactly how many Peruvians in the United States were trying to get back home, but estimated that it was about 6,000. He described them as a mix of students, vacationers and temporary workers. He noted that Peru's government was trying to help its citizens stranded in other countries return as well while Peru imposes a full shutdown of its borders and airports.

Asked about criticism that Peru was essentially taking Americans hostage until its citizens were brought back, Pereira said, "No, that's not the case." He said it was simply a matter of reciprocity. "It's a two-way conversation," he said. He did not immediately respond to a follow-up question about whether Peru will cover the cost of the flights.

He also urged Americans stranded in Peru to visit websites his government has arranged if they need assistance.

Americans also remain stuck abroad in other countries, including Guatemala, which closed its borders this past week. The U.S. citizens there, having received little help from the embassy and unable to book flights home, are crossing the border with Mexico in droves to get to airports where planes are still taking off back to the U.S., several people on the ground told POLITICO.

The State Department on Friday began flying charter flights from Morocco, another hotspot for Americans stranded abroad, back to 10 different U.S. airports.

The U.S. government has made "individual efforts" to bring home about 3,000 Americans since the outbreak began affecting flight service, Vice President Mike Pence said at a Saturday afternoon White House press briefing on the coronavirus pandemic.

"I think there is an ongoing effort to address that with chartered commercial flights that the government is providing," Pence said. Military transport is also available, he said.

"We would just encourage any American that is looking on from overseas, contact the local U.S. Embassy," Pence said. "Let them know about your circumstances. And know that we're going to work, continue to work very diligently to get our Americans home."