US authorities said two people with ties to the Islamic State group are due in court on Friday in California and Texas, including a refugee from Syria accused of returning there to fight alongside IS.

The arrests come amid heightened security in the US following last month's assault by a radicalised Muslim couple in California that left 14 people dead and the November terror attacks in Paris.

The attacks added to pressure for more scrutiny of refugees from war-ravaged Syria.

Aws Mohammed Younis al-Jayab, an Iraqi-born Palestinian arrested Thursday who came to the US from Syria as a refugee in 2012, travelled to Syria the following year where he fought for various terror groups, according to a criminal complaint.

One of those groups was Al-Qaeda affiliate Ansar al-Islam (Partisans of Islam), which previously operated under its own banner in Iraq and Syria.

Listed as a terrorist organisation by the UN and the US, its Iraqi faction has since merged with the Islamic State group, though some of its Syrian fighters rejected IS.

US Attorney Benjamin Wagner was careful to stress that "while (Jayab) represented a potential safety threat, there is no indication that he planned any acts of terrorism in this country."

Another Iraqi-born Palestinian, Omar Faraj Saeed Al Hardan, was indicted Wednesday in Texas for providing material support to the IS group. He is due to make an initial court appearance on Friday.

Hardan, 24, was charged with one count each of attempting to provide material support to ISIL (Islamic State), procurement of citizenship or naturalization unlawfully and making false statements.

Texas Governor Greg Abbott and other local officials said Hardan's arrest backed their calls for a refugee ban.

"This is precisely why I called for a halt to refugees entering the US from countries substantially controlled by terrorists," he said.

The state's Attorney General Ken Paxton called the arrest a "troubling revelation," using the occasion to take a swipe at President Barack Obama.

"The arrest in Houston of an Iraqi refugee for suspicion of terrorist activities is a troubling revelation - especially in light of the president's insistence on placing further refugees in Texas," he said.

"My office will continue to press for the right of Texans to ensure that terrorists are not being placed in our communities."

From refugee to radical  

Hardan, who lives in Houston, was granted legal permanent resident status in 2011, two years after entering the US.

According to the indictment, he provided training, expert advice and assistance to IS.

He also lied on his formal application to become a naturalized US citizen, saying he was not association with a terror group despite having been associated with IS members and sympathisers throughout 2014.

During an October 2015 interview, Hardan is also said to have falsely claimed he had never received weapons training of any kind when he had in fact learned to use machine guns.

He faces up to 53 years in prison and a $250,000 fine if convicted on all charges.

The complaint against Jayab, the 23-year-old Californian man, states that he planned his trip to Syria through online contact with various individuals and arrived there via Turkey in November 2013.

His online messages, copies of which are contained in the complaint, indicate he was based in the northern Syrian city of Aleppo, where he boasted about his activities with Ansar al-Islam, claiming he had also fought with the group while living in Iraq.

At one point, he apparently expresses interest in joining IS.

"I have been thinking of joining the State and abandon(ing) the al-Ansar," he says in one online message to an unidentified individual.

Authorities say Jayab crossed from Syria back into Turkey on January 17, 2014 and returned to California six days later.

He told immigration officials at the time that he had travelled to Jordan and Britain.

When further questioned by authorities about his travels, he stated he had gone to Turkey for a vacation and denied going to Syria.

Jayab, who also faces an initial court appearance on Friday, in California's state capital Sacramento, faces up to eight years in prison and a $250,000 fine if convicted of making a false statement involving international terrorism.