Murad Khaled al-Assidah, 18, was arrested in December and pleaded not guilty to a charge of threatening violence to disturb the Jordanian public.
Al-Assidah plans to appeal the verdict, his lawyer Majid Liftawi said.
In Tuesday's brief hearing, military court presiding judge Colonel Fawaz Buqur initially sentenced the defendant to five years in jail, but immediately commuted the sentence to two and a half years, telling al-Assidah it was to "give you a chance to repent".
Authorities said al-Assidah sent threatening e-mails to Jordanian intelligence officials because he thought they had allegedly prevented mujahidin, or Muslim fighters, from attacking Americans and Israelis.
According to an indictment, some of the emails contained hoax threats that a building belonging to the General Intelligence Department had a "modern and undetectable booby trap".
The indictment said al-Assidah once wrote: "With God's grace we succeeded in reaching New York, at the centre of the century's tyrant - America."
In a previous hearing, al-Assidah claimed his confessions had been forced, and that Jordanian investigators had threatened to rape him "if I didn't admit that I was the man who sent the e-mails".
Al-Assidah is from Zarqa, hometown of Abu-Musab al-Zarqawi, al-Qaida's point man in Iraq.
But the indictment said that al-Assidah never met al-Zarqawi, although he was in contact in 2003 with an Muslim activist identified as Abu Jamil living in the West Bank.
"With God's grace we succeeded in reaching New York, at the centre of the century's tyrant
email allegedly sent by Murad Khaled Al-Assidah
In a separate trial on Tuesday, four men charged with plotting to carry out attacks and the illegal possession of automatic weapons, pleaded not guilty at the opening of their trial.
According to the charge sheet, Mamduh Abu-Lubeh, Sufyan al-Samarah, Ghaleb Jafal Ibrahim and Yusuf al-Jaghameen allegedly plotted to attack foreigners in the southern city of Aqaba, 350km south of Amman, and to destroy liquor stores in the capital Amman and its suburbs.
The hearing was adjourned until 23 May.