The arrests feed a national debate over whether the United State is doing enough to screen refugees from Syria for terrorists from that nation.
Court documents say the men wanted to assist terrorist organizations affiliated with the Islamic State, though one man is accused of assisting a group that allied with Islamic State after he had returned to the United States.
US Attorney Benjamin Wagner said in a statement that while Al-Jayab was potentially dangerous, there is no indication that he planned any attacks in the United States.
Meanwhile, the US 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 the Islamic State.
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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.
"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."
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.
While living in Arizona and Wisconsin, he 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.
He left the United States in November 2013, but he came to Sacramento in January 2014, the FBI said in a 20-page affidavit.