The alleged ringleader, Mohammed Hassan al-Sehli, a 53-year-old Syrian, and his three sons appeared on Wednesday at a state security court along with Syrian businessmen Abdul Aziz al Jader, 52, and Jordanian Sameh Nobani, 23.
They all pleaded not guilty to three charges of "conspiracy to wage terror attacks that caused death of an individual and possession of explosives to use illegally and acts to undermine relations with a foreign country".
The suspects face the death penalty if found guilty.
"This is unjust. We are innocent," said a bearded al-Sehli, in blue prison uniform with his hands and feet cuffed in the dock of the court, which met at a maximum security prison.
Four Iraqis and two other al-Sehli sons, who prosecutors say arrived in Jordan from Iraq shortly before the August 19 attack, are also on trial in absentia. The suspects used Chinese-made Katyusha rockets, which they smuggled from Iraq.
The attack, which narrowly missed the USS Ashland and its sister ship the USS Kearsarge, was the most serious on US targets in Jordan since the killing of US diplomat Lawrence Foley in Amman in 2002.
Prosecutors said the suspects had initially planned to attack the heavily fortified US embassy in the capital, Amman.
They sought to hit the Israeli port of Eilat from nearby Aqaba but again changed their minds when they were drawn by the warships docking in the port, a logistics hub and a main supply base for US forces in Iraq.
The three rockets they fired by remote control barely missed the Ashland but hit a warehouse and a hospital, killing one Jordanian soldier and wounding another.
Prosecutors say al-Sehli, a car merchant, had sent his sons to fight US forces in Iraq to become battle hardened with the help of Iraqi Sunni insurgents. He was driven by desire for retaliation for Jordan's support for the US-led invasion of Iraq.