(CNN) Two refugees arrested this week on federal terrorism-related charges were in communication with each other, a law enforcement official told CNN.

Both men are Palestinians who were born in Iraq and came to the United States as refugees, according to the U.S. Justice Department. And both are accused of lying to immigration officials about their alleged ties to terrorist organizations. The two men were arrested Thursday.

Omar Faraj Saeed Al Hardan, 24, of Houston, was charged with attempting to provide material support to ISIS.

Citing social media communications, the criminal complaint against Jayab said he spoke with an unnamed Texas resident about weapons and training in Syria. That unnamed individual is Hardan, according to the law enforcement source.

"I need to learn from your weapon expertise," the individual wrote to Jayab, according to the complaint.

In his reply, Jayab wrote, "We will make your abilities very strong," according to authorities.

"Our concern now is only to arrive there," Jayab went on. "When you arrive to al-Sham [Syria] you will be trained."

It was not immediately clear whether Hardan or Jayab had retained legal representation. They are both scheduled to appear in court Friday.

Suspect's brothers, cousin charged

Also on Friday, federal authorities in Milwaukee announced that three of Jayab's relatives had been accused of trying to transport stolen cellphones and computers across a state line.

Jayab's brothers, Younis Mohammed Al-Jayab and Samer Mohammed Al-Jayab, and their cousin, Ahmad Waleed Mahmood, were all charged with conspiracy, interstate transportation of stolen property, receiving stolen property and aiding and abetting, according to the criminal complaint.

The three men thought they were buying stolen merchandise -- 32 Apple iPhones, a laptop computer and a television -- from a man who turned out to be an undercover agent, the complaint said.

Authorities intercepted other phones that Younis Mohammed Al-Jayab tried to mail to Cyprus and Romania, the complaint said.

Samer Mohammed Al-Jayab was arrested in California and is undergoing a removal process, CNN affiliate WTMJ reported. The other two suspects appeared Friday in federal court in Milwaukee and were released without bond after surrendering their passports and being ordered to stay in the eastern district of Wisconsin, WTMJ reported.

Should U.S. accept refugees with Syrian ties?

The arrests come as some Americans worry that terrorists could enter the United States posing as refugees from war-torn nations.

"This is an extraordinary snapshot of what we're facing now -- the challenge of vetting individuals and maintaining the beacon of hope that America has been for the world over," said Michael Wildes, an immigration attorney and former federal prosecutor.

The concerns about refugees were amplified after the Paris terror attacks in November. ISIS claimed responsibility for those coordinated attacks on a concert hall, bars, restaurants and a sports stadium that killed 130 people.

White House Press Secretary Josh Earnest described the arrests as good examples of how law agencies "work effectively together to keep us safe."

But he noted the political controversy about whether the United States should accept refugees with Syrian ties.

"I know these kinds of situations are likely to prompt calls from the other side that are familiar, to suggest that the United States should impose a sort of religious test or a test based on an individual's ethnicity to limit their ability to enter the United States," Earnest said.

"That doesn't represent who we are as a country and most importantly, it's not going to keep us safe," Earnest said.

After news of Hardan's and Jayab's arrests Thursday, Sen. Ted Cruz, a Republican presidential candidate, reiterated his views that the United States should not accept refugees from Syria and called for a "systematic and careful retroactive assessment" to determine whether or not refugees already in the United States have ties to terrorists.

"I commend the law enforcement for apprehending these two individuals, but their apprehensions raise the immediate question: Who else is there? What are they planning next?" Cruz said.

Wildes said Cruz's comments were "off-key."

"We cannot forget that legacy that we have for immigration. We are a safe haven. Our Founding Fathers established this nation with a notion that it will be a place for safety," Wildes said.

Texas man aimed to support ISIS, indictment alleges

Hardan entered the United States as an Iraqi refugee in November 2009 and was granted legal permanent resident status in August 2011, the Justice Department said.

In addition to the charge of attempting to provide material support to ISIS, he's charged with procurement of citizenship or naturalization unlawfully and making false statements.

A federal grand jury indictment unsealed Thursday alleges he attempted to provide material support and resources, including training, expert advice and assistance, to ISIS. The indictment does not provide details about the evidence behind the allegations.

The indictment also alleges he lied in his citizenship application, saying he had no ties to a terrorist organization when he'd associated with members and sympathizers of ISIS throughout 2014, according to the Justice Department.

If convicted, Hardan faces a maximum sentence of 20 years in prison and a $250,000 fine.

Complaint: Social media posts revealed terror ties

Jayab entered the United States as a refugee, emigrating from Syria, in October 2012, the Justice Department said.

According to a criminal complaint filed in federal court, Jayab exchanged messages on social media in 2012 and 2013, saying he planned to go to Syria to fight.

In November 2013, the complaint alleges, he flew from Chicago to Turkey, then traveled to Syria. Between November 2013 and January 2014, he "allegedly reported on social media that he was in Syria fighting with various terror organizations, including Ansar al-Islam," officials said.

Asked about his travel in an interview with U.S. Citizenship and Immigration Services, Jayab allegedly said he had traveled to Turkey to visit his grandmother and denied he had been a member of any rebel group or militia.

In a written statement, U.S. Attorney Benjamin Wagner said there were no signs that Jayab was involved in any U.S. terror plots.

"While he represented a potential safety threat, there is no indication that he planned any acts of terrorism in this country," Wagner said.

If convicted, he faces a maximum penalty of eight years in prison and a $250,000 fine.