AUSTIN, Texas (AP) — As he ended Texas’ coronavirus restrictions Wednesday over the objections of public health officials, Republican Gov. Greg Abbott has tried shifting concern about the virus’ spread to migrants with COVID-19 crossing the U.S.-Mexico border, though without evidence they are a significant factor.

The focus by Abbott and other Republicans on migrant families has drawn criticism about invoking a long history in the U.S. of wrongly suggesting migrants spread diseases.

Twin pressures are bearing down on the Texas border as, beginning Wednesday, state residents no longer are required to wear face coverings after eight months under a mask mandate. Infection levels remain higher in the region than in most others, and rising numbers of immigrants are now overwhelming federal detention facilities.

Arriving migrants who test positive are being directed to local hotels for isolation, as Abbott and Democratic President Joe Biden fight over who is responsible for helping them.

Doctors on the border fear Abbott repealed coronavirus safeguards too soon and threatens a fragile decline in COVID-19 cases. The surge of immigration to the border is also worrying, they say, but far from the biggest factor in containing the virus’ spread.

“It’s not trivial,” said Dr. James Castillo, the public health authority for Cameron County in Texas’ Rio Grande Valley, the busiest corridor for migrant apprehensions along the U.S.-Mexico border.

“Is it the biggest source of infection to our whole community?” he said, referring to migrants arriving with the virus. “No, it’s maybe one source, and there’s a lot of different sources. And it’s a shame that we’re going to create new sources by dropping the restrictions.”

Abbott, under pressure from conservatives to end COVID restrictions, announced last week that Texas would fully reopen, allowing full capacity in restaurants and bars and large gatherings that had been considered dangerous. Biden criticized the decision as “Neanderthal thinking,” and Abbott shot back by alleging Biden was “releasing COVID-positive illegal immigrants in our state” by easing some of former President Donald Trump’s toughest border policies.

Abbott has rejected offers from the Biden administration for help with testing and quarantining migrants, saying that job belongs entirely to the federal government.

“The federal government has the responsibility to fund the testing of anybody coming here who does have COVID,” Abbott said during a trip to the border Tuesday.

Asked whether the governor had numbers on migrants with COVID-19 who have entered the U.S., Abbott spokesman Renae Eze offered a statement Wednesday: “Because the Biden Administration has refused to step up and do their job, we may never know the true total of COVID-positive illegal immigrants and the impact on our state and our country.”

The Department of Homeland Security said it would fully fund testing, isolation, and quarantine of migrants, but that Abbott needed to sign off.

“We hope that Governor Abbott will reconsider his decision to reject DHS’s agreement with the Texas local authorities that would enable the very testing of migrant families that Governor Abbott says he wants,” the agency said.

There are three types of immigrants entering in South Texas, according to border authorities: People who were in Trump’s “Remain in Mexico” program who were waiting for immigration court dates and must test negative, children who are unaccompanied by a parent or guardian who are referred to U.S. Health and Human Services, and migrant parents with young children that the Border Patrol releases quickly. Some cities are getting hundreds of migrant families daily.

Two HHS contractors in Texas who were not authorized to speak to the media say the positivity rates for children are generally 8% or below, which is lower than the current statewide test rate. Children who test positive are isolated until they are clear of the virus.

The infection rates for all arriving immigrants are lower than for Texas as a whole, local officials and nonprofit groups serving those families say.

In the border city of Brownsville, Mayor Trey Mendez said last week that about 6% of immigrants tested positive at the local bus station. In McAllen, Sister Norma Pimentel of the local Catholic Charities chapter said around one family in a group of 100 people typically tests positive and is directed to isolate in a local hotel.

Both Cameron and Hidalgo counties — where Brownsville and McAllen are located — currently have test positivity rates of about 10%.

Many cities and local groups need more help as more immigrants arrive, hoping their chances of entry to the U.S. are better under the new administration.

In Del Rio, a nonprofit group called the Val Verde Border Humanitarian Coalition received nearly 200 people in the first few days of March alone, after receiving more than 460 people in all of February.

Dr. Ivan Melendez, the health authority in Hidalgo County, said now about 10 people a day are dying there instead of 50. He criticized Abbott for lifting the mask mandate but said the arrival of migrants is also a concern.

“The reality of it is you cannot have an influx of thousands of people in your community during a pandemic,” he said.

U.S. Rep. Henry Cuellar, a longtime border Democrat from Laredo, Texas, criticized the Biden administration for rolling back some Trump-era immigration policies too quickly and opening more holding facilities too slowly.

“Once you’re the president, you own the failure or you own the success,” he said.

But Cuellar also criticized people “who try to invoke fear” about immigrants, particularly children.

“If you’re afraid of a little kid, a 7-year-old, then I think you fear your own shadow,” he said.