The U.S. Homeland Security chief has flatly denied that ISIS members crossed the Mexican border into Texas – as conservative lawmakers claimed – but did admit that four Kurdish terrorists did slip through.

DHS Secretary Jeh Johnson was forced to deny that 10 people linked to ISIS had entered Texas after Republican Representative Duncan Hunter made the startling claim on Fox News on Tuesday.

But on Thursday, Johnson conceded that four members the Kurdistan Workers' Party, known as the PKK, were arrested in September trying to enter the United States illegally from Mexico.

The PKK, a separatist group in Turkey, is deemed a 'foreign terrorist organization' by the U.S. government – but it has allied itself with other Kurdish groups fighting ISIS.

Denial: U.S. Secretary of Homeland Security Jeh Johnson, who is pictured last week, denied that ISIS terrorists had been captured at the Mexico-Texas border but said four anti-Islamic fighters were arrested last month

In his speech at the Center for Strategic and International Studies, Johnson noted that the PKK was 'actually fighting against ISIL and defended Kurdish territory in Iraq'.

They had been arrested for unlawful entry, detained and would be deported by U.S. authorities, he said in a speech in Washington.

But in an interview with CBS News, Rep. Jason Chaffetz of Utah stood by his concerns, noting that the PKK has been designated a foreign terrorist organization by the State Department.

'I don't think that should be dismissed as insignificant,' he said in the earlier interview. 'It does demonstrate how porous or our border is. These are terrorists nonetheless and they had no trouble crossing our southern border. That's a problem that must be addressed.'

He claimed that the men flew into Mexico City, hired someone to smuggle them across the Rio Grande and then get them to a safe house.

They intended to make their way to New York City, although there is no specific indication they were here to commit a terrorist act, he said.

Fears: Rep. Duncan Hunter stunned a Fox News audience earlier this week by saying that the US has apprehended about ten ISIS terrorists as they entered the country through the Mexican border

Several conservative politicians and media outlets have claimed in recent days that Islamic State militants had infiltrated the United States from Mexico, which Johnson and other administration officials have denied.

On Tuesday, Representative Duncan Hunter, a California Republican, told Fox News that 'at least 10 ISIS fighters have been caught coming across the Mexican border in Texas'.

He added: 'ISIS doesn't have a navy, they don't have an air force, they don't have nuclear weapons. The only way that ISIS is going to harm Americans is by coming in through the southern border -which they already have.'

Hunter said his information came directly from U.S. Customs and Border Protection, which has a 20,000-strong army of agents patrolling the borders in Texas, Arizona, New Mexico and California.

'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 Homeland Security spokesman said in a statement.

Vulnerable: Much of the Texas-Mexico border is undefended, with US Border Patrol agents setting up well on the American side. In September, four men from an anti-Islamic Kurdish party entered the country

A second Republican, Representative Tom Cotton, a Senate candidate in Arkansas, said last month that the Islamic State was collaborating with Mexican drug cartels.

But U.S. intelligence and national security officials said that U.S. agencies had no evidence that anyone connected with the Islamic State or other jihadist groups fighting in Iraq or Syria have tried to cross into the United States from Mexico.

The officials also said they were unaware of any threat or plots by the Islamic State or related groups coming from Mexico.

Hunter, like many in the GOP, has advocated in the past for strengthening America's border security to the south, a demand that has largely fallen on deaf ears during the Obama presidency.