A Republican congressman claimed Tuesday that "at least 10" Islamic State "fighters" have been caught trying to cross the U.S.-Mexico border into Texas, though an administration official denied it.

Rep. Duncan Hunter, R-Calif., said he learned the information from the Border Patrol, warning that the alleged attempts to cross into the U.S. raise serious security concerns.

"ISIS is coming across the southern border," he told Fox News. "They aren't flying B1 bombers bombing American cities, but they are going to be bombing American cities coming across from Mexico."

Hunter continued: "I know that at least 10 ISIS fighters have been caught coming across the Mexican border in Texas."

He claimed Border Patrol "caught them," but "you know there's going to be dozens more that did not get caught by the Border Patrol."

The Department of Homeland Security on Wednesday denied Hunter's claim.

"The suggestion that individuals who have ties to ISIL have been apprehended at the Southwest border is categorically false, and not supported by any credible intelligence or the facts on the ground," a senior DHS spokesman said. "DHS continues to have no credible intelligence to suggest terrorist organizations are actively plotting to cross the southwest border."

But Hunter spokesman Joe Kasper said the information -- that about 10 individuals with "known ISIS affiliations" -- came from a "high-level source within the Border Patrol."

"The congressman was conveying what he knows -- and what he was told," Kasper said. "It makes sense that the left hand of DHS doesn't know what the right hand is doing -- it's been that way for a long time and we don't expect that to change."

Obama administration officials previously have downplayed the threat of Islamic State militants infiltrating the U.S. through the southern border, as warnings about that possibility have circulated.

Homeland Security Secretary Jeh Johnson, in an interview with Fox News last week, acknowledged reports that four men with suspected terror ties had been apprehended at the southern border in Texas and questioned. But Johnson said they were "scrutinized very, very carefully" and officials found "no evidence that these individuals were tied to terrorism."

Border Patrol and Homeland Security sources also told Fox News that they have not been able to substantiate Hunter's claim. They said between Sept. 23 and Oct. 6, only five illegal immigrants from "special interest" countries were arrested at the Texas border -- and they were from Bangladesh.

The four men that Johnson referred to were actually Kurds, Fox News is told.

Johnson, at a hearing last month, stressed that the government had "no specific intelligence or evidence to suggest at present that ISIL is attempting to infiltrate this country though our southern border."

At the same hearing, National Counterterrorism Center head Matthew Olsen also said: "There has been a very small number of sympathizers with ISIL who have posted messages on social media about this, but we've seen nothing to indicate there is any sort of operational effort or plot to infiltrate or move operatives from ISIL" into the U.S. through the southern border.

Still, Johnson said the U.S. needs to be "vigilant" and aware of the possibility of "potential infiltration by ISIL or any other terrorist group."

The union representing America's immigration caseworkers also sounded an urgent warning last month about the threat. Kenneth Palinkas, president of the National Citizenship and Immigration Services Council, alleged the administration has made it easier for terrorists to "exploit" the country's visa policies and enter the homeland.

He complained that the administration has "widened the loophole" they could use through the asylum system, and has restricted agents from going after many of those who overstay their visas.

Further, he warned that executive orders being contemplated by President Obama would "legalize visa overstays" and raise "the threat level to America even higher." He said there is "no doubt" many are already being "targeted for radicalization."

FoxNews.com's Judson Berger and Fox News' Jennifer Griffin and William La Jeunesse contributed to this report.