Two Iraqi-born men were arrested Thursday in Houston and Sacramento in an ongoing terrorism investigation, according to prosecutors.

In a statement late Thursday, the U.S. Attorney's office in Sacramento identified the suspect there as Aws Mohammed Younis Al-Jayab, 23, who faces a federal charge of making a false statement involving international terrorism.

"According to the complaint, Al-Jayab is a Palestinian born in Iraq, who came to the United States as an Iraqi refugee in October 2012," the statement said.

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"Between November 2013 and January 2014, Al-Jayab allegedly reported on social media that he was in Syria fighting with various terrorist organizations, including Ansar al-Islam, a designated foreign terrorist organization since 2004," authorities said. "He returned to the United States on Jan. 23, 2014, and settled in Sacramento."

When he was interviewed by U.S. citizenship officials, Al-Jayab lied about his travel, claiming he went to Turkey to visit his grandmother, the criminal complaint said.

A Department of Justice statement said Omar Faraj Saeed Al Hardan, 24, also a Palestinian born in Iraq, was arrested in Houston. Al Harden, who has lived in the U.S. since 2009, is charged with one count each of attempting to provide material support to ISIS, procurement of citizenship or naturalization unlawfully and making false statements.

A law enforcement source told CBS News Justice and Homeland Security correspondent Jeff Pegues authorities believe Al Harden became radicalized during his time here in the U.S.

An third arrest Thursday in Milwaukee was not related to terrorism, the DOJ told CBS News' Paula Reid.

Texas Gov. Greg Abbott weighed in on the case Thursday, releasing a statement before federal authorities had concluded their investigation.

"I applaud the FBI for today's arrest of this dangerous subject," Abbott said. "However, this is precisely why I called for a halt to refugees entering the U.S. from countries substantially controlled by terrorists. I once again urge the President to halt the resettlement of these refugees in the United States until there is an effective vetting process that will ensure refugees do not compromise the safety of Americans and Texans."

"Based on the facts, as we know them, today's action may have prevented a catastrophic terror related event in the making and saved countless lives," Lt. Gov. Dan Patrick said in a statement.