Two Yemeni men arrested in Saudi Arabia and extradited to the United States face federal charges of conspiring to attack U.S. soldiers in Iraq and Afghanistan, The New York Times reported.

Both men were arraigned, separately, this week before magistrates in the U.S. District Court for the Eastern District of New York in Brooklyn.

Authorities had sought to bring the men, identified as Saddiq Al-Abbadi and Ali Alvi, to justice since at least 2009.

Abbadi operated in both Iraq and Afghanistan starting in 2003, ambushing convoys and planting improvised explosive devices. Alvi shifted allegiances from al-Qaida to the Taliban in Afghanistan.

Abbadi and Alvi have been charged with providing material support to al-Qaida and conspiracy to murder American nationals abroad, the Times reported.

Abbadi is believed to be well-connected to the al-Qaida leadership. He brought Bryant Neal Vinas, now a government witness, into al-Qaida and arranged for his weapons training.

Vinas facilitated a plot to blow up a Long Island Rail Road commuter train in Manhattan's Pennsylvania Station, the Times said.

Vinas, a Hispanic convert to Islam from Long Island, N.Y., traveled to Pakistan for military training. He was captured by Pakistani forces at the United States' request and turned over to American authorities.

The criminal complaint notes that al-Qaida maintains "training facilities and safe houses" in Pakistan's tribal areas, where recruits can study bomb-making, the Times reported.

A federal prosecutor said that the case will likely involve secret intelligence information, according to the Times.

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