The four Kuwaitis said statements admitting to plots to attack Iraq and Kuwait were extracted under physical and mental torture.
"We demand that our interrogation be repeated since we were forced to say what did not happen and things that we had nothing to do with," Hamad al-Harbi, Muhammad al-Asfur, Ahmad al-Utaibi and Badr al-Utaibi said in a joint statement in Kuwait City on Friday.
The four men were arrested in August on suspicion of being al-Qaida supporters and running a local network of young people with radical religious ideas seeking to fight US forces in Iraq and Kuwait.
Kuwaiti officials were not available for comment.
The men, released earlier this month pending trial, told a news conference in the capital that after being arrested, they were handed over to state security officials and "most of us were subjected to beatings, torture and continuous insults".
"In this particular case, they asked a person to confess to incriminate himself and others he may not even know beforehand."
Most were ordered to repeat their fabricated confessions at the public prosecutor's office under threat of being mistreated, the men said.
They were held in isolation in prison and went on hunger strike for three days in protest, but were ordered to stop or face further abuse, they added.
The four men demanded that members of the Kuwaiti Parliament should publicly question Interior Minister, First Deputy Prime Minister Shaikh Nawaf al-Ahmad al-Sabah and Justice Minister Ahmad Baqar about the allegations.
"Such transgressions should not exist in a country that claims to have freedoms and to protect human rights," they said.
"If trust in the judiciary is lost then citizens and residents will have no trust in anything else."
Kuwait has tightened security after a surge in violence in Iraq and Saudi Arabia.
It has also cracked down on groups opposed to the presence of foreign troops, and has launched a state-wide awareness programme to combat what it calls religious extremism.