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Federal authorities have arrested two men accused of having ties to ISIS on terrorism-related charges in California and Texas, including a refugee from Syria who is charged with lying to federal investigators about his travels to the civil war in that country.

There was no plot to carry out attacks within the United States, one law enforcement official told NBC News on Thursday, while another federal official added that there was never any real danger to Americans.

A criminal complaint unsealed Thursday accuses Aws Mohammed Younis Al-Jayab, 23, of Sacramento, of traveling to Syria to fight and then lying to investigators about it.

Prosecutors say he assisted a group that allied with ISIS.

Meanwhile, the U.S. Attorney's Office based in Houston, Texas, said late Thursday that Omar Faraj Saeed Al Hardan, 24, of Houston, was indicted Wednesday on three charges that he tried to provide material support to extremists.

Read the Criminal Complaint Against Al-Jayab

Read the Criminal Complaint Against Al Hardan

Both men are Palestinians born in Iraq, authorities said. The complaint in federal court in Sacramento said Al-Jayab came to the United States from Syria as a refugee in October 2012. Court documents suggest he was already allied with terror groups when he arrived. But there's no suggestion that al Hardan was radicalized when he came to the U.S. six years ago as a 17-year-old refugee.

There is no indication from prosecutors that Al Hardan was a threat in the United States, but his arrest sparked immediate criticism of the Obama administration's refugee policies from Texas Gov. Greg Abbott and Lt. Gov. Dan Patrick.

Texas Governor Greg Abbott. DESMOND BOYLAN / AFP - Getty Images

"This is precisely why I called for a halt to refugees entering the U.S. from countries substantially controlled by terrorists," Abbott said in a statement. "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."

While living in Arizona and Wisconsin, Al-Jayab communicated on social media about his intent to return to Syria to fight for terrorist organizations and discussed his previous experience fighting against the regime in Syria, starting shortly after he turned 16.

When he was interviewed by citizenship officials, he lied about his travels and ties, the complaint alleges.

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In 2013, investigators say Al-Jayab wrote online that he was "eager to see blood."

He left the United States in November of that year, but he came to Sacramento in January 2014, the FBI said in a 20-page affidavit.

Social media and other accounts say that as soon as he arrived in the United States in 2012, he began saying he wanted to return to Syria to "work," which the FBI says is believed to be a reference "to assisting in and supporting violent jihad."

Authorities said he eventually fought with various terrorist organizations, including Ansar al-Islam, which in 2014 merged with ISIS after Al-Jayab had returned to the United States.

But Al-Jayab also criticized ISIS in several messages for killing Muslims.

"If it weren't for the State's bloodletting, I would have been the first one to join it," he said, according to the FBI, although he later described fighting alongside the group.

The documents did not indicate how Al-Jayab and Al Hardan are connected.

However, the affidavit says Al-Jayab communicated with an unnamed individual living in Texas in April 2013 to see if he could receive training in various weapons. Federal authorities tell NBC News that individual was Al Hardan.

A few days later, Al-Jayab described, during earlier fighting, emptying seven ammunition magazines from his assault rifle during a battle and executing three Syrian government soldiers.

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"Seven magazines in one breath ... Just shooting, spraying, spraying," Al-Jayab wrote to someone online, investigators added.

One Iraqi refugee who knew Al-Jayab told NBC affiliate KCRA that he was surprised by the arrest.

"Maybe he would get angry at times but he would never say anything related to terrorism. He was a nice decent person to me," the refugee said.

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Ben Galloway of the federal defender's office is Al-Jayab's attorney. He did not return telephone and emailed messages Thursday to The Associated Press.

The U.S. Attorney's Office in Sacramento said Al-Jayab was arrested Thursday morning in Sacramento.

Federal officials say three separate arrests in Milwaukee on Thursday grew out of the Sacramento investigation but are not related to national security.

The suspects in Wisconsin are relatives of the man arrested in Sacramento, said Lauren Horwood, a spokeswoman for the U.S. Attorney's Office in Sacramento.