Washington had committed a "serious mistake" and brought charges against Imam Muhammad Ali al-Muayad and Muhammad Muhsen Yahya Zayid "without any proof", an anonymous government official said in the Yemen capital Sanaa on Sunday.
The official deplored "the obstinacy of the American authorities in persisting in their error".
The pair, who were caught in a sting in Germany, appeared for a preliminary hearing in a district court in Brooklyn, New York, in November on charges of conspiring to provide material support to al-Qaida and the Palestinian resistance group Hamas.
They were arrested by Germany's Bundeskriminalamt (BKA) in January 2003, in Frankfurt, at the request of the US Department of Justice and the Federal Bureau of Investigation.
Al-Muayad is said to have been a finance chief for Usama bin Ladin's al-Qaida and Hamas, supplying both organisations with weapons and communications equipment.
He has also been linked to the October 2000 attack on the destroyer USS Cole in Yemen which killed 17 crew and injured 38.
Zayid was charged as an accomplice.
The authorities in Yemen have repeatedly demanded they should be returned to Sanaa.
Washington has also branded another senior Yemeni figure a "terrorist", prompting Yemen to demand proof of accusations against Abd Al-Majid al-Zindani, the head of the central committee of Yemen's leading opposition Islamist party Al-Islah.