"I plead with the court... to carry out the maximum penalty, death by hanging in public," said Ashraf al-Akhrass during the trial on Monday.
Minutes earlier Iraqi-born Sajida al-Rishawi, the sole defendant behind bars, denied any wrongdoing and when asked by the president of the court if she was guilty she responded: "No".
Akhrass' father and father-in-law were among 60 people killed in simultaneous suicide attacks on three Amman hotels on November 9, 2005.
His mother-in-law later died of her injuries.
The attacks were claimed by the al-Qaeda group in Iraq led by Jordanian-born militant Abu Musab al-Zarqawi.
60 people were killed in the attacks
on three Amman hotels
Rishawi's court-appointed lawyer Hussein al-Masri protested Akhrass' call for a public hanging and told him he was being "emotional" while there was no comment from the court.
Hangings are carried out behind prison walls in Jordan, which has executed three convicts this year, including two hanged in connection with the murder of a US diplomat in 2002.
Masri also asked the court for a medical evaluation of his client, arguing that she suffered psychological problems and may not understand the charges against her.
But the president of the tribunal backed the position of the state prosecutor and denied the request.
"The accused was partner to a conspiracy and had in her possession an explosives belt which she planned to use in an illicit fashion," the state prosecutor said.
"I plead with the court... to carry out the maximum penalty, death by hanging in public"
Ashraf al-Akhrass, who lost three family members, at the trial of Sajida al-Rishawi
"She was aware of what she did, she tried to blow herself up but, thanks be to God, she failed in her attempt," the prosecutor added.
Rishawi was arrested four days after the bombings and later confessed in footage broadcast on state television how she tried but failed to activate an explosives belt at the Radisson SAS hotel - one of the three bombed - where the Akhrass wedding was underway.
Her Iraqi husband, Ali Hussein al-Shammari, blew himself up in the attack.
Jordan has charged several suspects over the attacks, including Zarqawi, the most-wanted man in Iraq, who claimed responsibility for the bombings.
The trial was adjourned to May 22 after a 90-minute hearing during which five prosecution witnesses took the stand.
During the hearing, Rishawi showed little or no emotion, particularly when, at the request of her lawyer, the court observed a minute's silence in memory of the dead.