MEXICO CITY -- Border crossings by Venezuelans fleeing to the United States from their South American country plummeted in the first week of a U.S. policy to expel them to Mexico without an opportunity to seek asylum, U.S. and Mexican officials said Friday.

Biden administration officials said about 150 Venezuelans were crossing the border from Mexico daily, down from about 1,200 before the policy was announced Oct. 12.

Arturo Rocha, a top official in Mexico's Foreign Relations Department, said separately that Venezuelans entering the U.S. fell 90%, roughly in line with the U.S. government's numbers. He said the number of Venezuelans crossing the dangerous Darien Gap between Colombia and Panama on the most popular route to the United States dropped 80%.

The Panamanian government reported Friday that 435 Venezuelan migrants had flown back to their homeland from Panama since the U.S. announced the new rules. It said 200 more Venezuelans were expected to return Saturday on charter flights arranged by the Venezuelan consulate.

Biden administration officials said Venezuelans were generally being expelled under a public health rule known as Title 42, which suspends rights to seek asylum under U.S. and international law on grounds of preventing the spread of COVID-19. The White House expanded the policy to expel Venezuelans to Mexico despite an effort earlier this year to end Title 42, which has stayed in effect under a court order.

Under the new rules, the U.S. says it will accept up to 24,000 Venezuelan migrants at U.S. airports if they first apply online with a financial sponsor. They would be admitted on humanitarian parole in an effort similar to how tens of thousands of Ukrainians have entered the United States since Russia's invasion.

Rocha wrote in a newspaper column that the U.S. has received about 7,500 Venezuelan applications for parole. U.S. officials declined to confirm that number in a conference call with reporters but said there was significant interest and flights would begin soon.

While barely a week old, the crackdown on Venezuelans had immediate affect what had become a serious challenge for the Biden administration. Venezuelans were the second-largest nationality to cross the border illegally from Mexico in August, with another sharp increase in September to more than 33,000.

Many Venezuelans who were headed to the U.S. when the new rules were announced are now in Mexico and are unsure what to do next.

Mexican officials discussed early results of the effort at joint exercises with Guatemala on controlling migration.

Even as that official event unfolded, migrants continued to cross the Suchiate River between the two countries on inner-tube rafts, but most quickly turned themselves in to Mexican agents.

Up to now, Mexico gave Venezuelans and other migrants short-term transit passes that allowed them to reach a town farther inside Mexico, San Pedro Tapanatepec, where they could wait for more formal visas.

Thousands of migrants had gathered in San Pedro Tapanatepec awaiting those papers, which many previously used to continue on to the U.S. border.

But on Friday, Hector Martinez Castuera, the director of coordination for Mexico's National Immigration Institute, said visas would no longer be handed out in San Pedro Tapanatepec. Instead, Mexican authorities set up a migrant shelter to handle all those waiting there.

"We have installed a shelter there, a big shelter to handle the migrants, but right now we are not giving out any immigration forms," he said.

Martinez Castuera said migrants could try to get papers to remain in Mexico or return to Venezuela. He said that Mexico may help some return, as "many Venezuelans" want, but that the issue was complicated.

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Spagat reported from San Diego.