New York (CNN) Two Yemeni nationals have been charged with aiding al Qaeda, authorities announced on Tuesday.

The criminal complaint alleges that Saddiq al-Abbadi and Ali Alvi provided material support to the terrorist organization and conspired to murder Americans abroad.

"There is no escape from the reach of our law for violent terrorists, especially if they target our military," Loretta Lynch, the U.S. attorney for the eastern district of New York, said in a press release . "Al-Abbadi and Alvi may have operated in the mountains of Afghanistan, but now they face justice in a courtroom in Brooklyn."

Both men were arrested in Saudi Arabia and then transferred to U.S. custody. Al-Abbadi had already served more than five years of a 12-year prison sentence in Saudi Arabia before he was handed over.

Judge Lois Bloom ordered al Abbadi be held without bail until his trial was completed, as he poses a danger to the community as an al Qaeda operative "with extensive weapon and explosives training," according to Zainab Ahmad, one of the prosecutors handling the case.

Both Alvi and al-Abbadi face a maximum sentence of life in prison, according to the release.

Al-Abbadi has not yet entered a plea in the case and his court-appointed defense attorney refused to add anything after the hearing.