A rising number of Russians and Ukrainians are coming to Mexico, purchasing used automobiles, and driving across the border into the United States to seek asylum, a trend that might escalate as Russia’s invasion of Ukraine has driven over a million people to abandon their homes.

According to Customs and Border Protection (CBP) data, border agents in the United States contacted around 6,400 Russians between October 2021 and January of this year. This is higher than the approximately 4,100 captured for the whole fiscal year 2021, which concluded on September 30. The increase among Ukrainians is comparable, with slightly more than 1,000 caught from October 2021 to January, compared to around 680 for the entire previous fiscal year.

These migrants account for a slim fraction of the 670,000 apprehensions made by U.S. border agents in the first months of the 2022 fiscal year, CBP figures show. The majority of those stopped were from Mexico and Central America and were swiftly removed from the United States.

Yet almost all the Russians and Ukrainians have been allowed to remain while they pursue asylum claims, and their presence has been notable at border-area shelters aimed at helping newcomers.

Since June, Russians have consistently been among the top three nationalities arriving at a San Diego shelter, according to data published by the San Diego Rapid Response Network, a coalition of nonprofits, attorneys and community leaders. Last week, Ukrainians were the third most-common nationality among arrivals.

The CBP figures include only migrants who arrived before Russia’s Feb. 24 invasion of Ukraine. But one current and one former border official who spoke with Reuters on condition of anonymity said there could be further increases as the fighting has intensified.

More than 1 million refugees have already fled Ukraine amid an onslaught of Russian tanks, troops and missiles that Russia has dubbed a “special operation.” Most have headed to neighboring European countries. But the sheer speed and size of the exodus will exert tremendous pressure on these hosts and likely push some further afield.

Russian President Vladimir Putin, meanwhile, has cracked down on dissent at home by jailing anti-war protesters and closing independent news outlets. Powerful financial sanctions by Western countries are already hammering Russian citizens, adding to migration pressures there.

Would-be migrants from Ukraine and Russia are swapping tips on social media on how to make the journey to the U.S. southern border via Mexico to claim asylum.

Russian dissident Dmitriy Zubarev made that trek last year. A civil rights lawyer, Zubarev had worked on the presidential campaign of Russian opposition leader Alexei Navalny, who is currently jailed. Spooked by the growing crackdown on dissent, Zubarev fled after Navalny’s organizations were labeled “extremist” by the Russian government.

Zubarev told Reuters he boarded a plane in June 2021 from Moscow to Cancun, Mexico, then flew to Tijuana at the U.S border where he boarded a minivan with 11 other migrants. As soon as he crossed over, he said he asked for asylum and was released to pursue his case. Zubarev currently resides in Connecticut. He predicted more Russians would follow.

“Repression is intensifying and the people coming out to protest the war are treated very harshly,” Zubarev told Reuters. “There will be more people trying to use refugee routes to escape the bad situation in the country.”

The Russian government did not immediately respond to a request for comment on Zubarev.

The Russian Embassy in an emailed statement said it was “very concerned” about what it characterized as “detention” of alleged Russian citizens at the U.S.-Mexico border near San Diego, and that it had contacted the U.S. State Department to verify their identities.

The State Department did not immediately respond to a request for comment.

U.S. President Joe Biden and his top officials have said they strongly support Ukrainians as well as Russians who have taken to the streets to protest the invasion.

But his administration so far is playing a secondary role to Europe when it comes to the refugee crisis, and has said it expects most fleeing Ukrainians to head to European nations.

The Biden administration on Thursday said it was granting temporary deportation relief and work permits to tens of thousands of Ukrainians already in the United States as of March 1.

At a congressional hearing on Wednesday, Representative Lou Correa, a Democrat from California, said he was taken aback by the number of Russian and Ukrainian migrants arriving by car when he visited the San Ysidro port of entry between San Diego and Tijuana about a month ago.

A border agent pointed out 20 cars that had been pulled over, saying they were full of Ukrainian and Russian migrants, Correa recalled.

“This problem is not going away,” Correa said.