The plaintiffs want the PA and the PLO held accountable for supporting the attacks, which included a bombing at a packed cafeteria at Jerusalem's Hebrew University, as well as suicide bombings and shootings on busy streets.
The attacks took place between 2001 and 2004 during the second Palestinian Intifada – or uprising – killing 33 people and injuring more than 390 others, including members of the 11 plaintiff families.
Plaintiffs filed the suit in US court because some of the victims were American citizens.
The attacks were carried out by members of Hamas and the Al-Aqsa Martyrs’ Brigades, some of whom were on the PA and PLO payrolls, Al Arabiya News reported.
"Those involved in the attacks still receive salaries from the Palestinian Authority and still get promoted in rank while in jail," said Nitsana Darshan-Leitner, of the Israel-based Shurat HaDin Law Center, a lawyer who is representing the victims' families.
Families of suicide bombers receive monthly salaries from the Martyrs’ Brigades, she added.
Lawyers for the Palestinian Authority argued that it should not be held responsible for the attacks committed by bombers and gunman who acted on their own, Al Arabiya News reported.
— #Gaza #FreePalestine (@leilanazzar) February 1, 2015
“It is not the right thing to hold the government liable for some people doing crazy and terrible things,” defense attorney Mark Rochon said in his closing argument.
“There is no conclusive evidence that the senior leadership of the PA or PLO were involved in planning or approving specific acts of violence.”
Earlier this year, Meshulam Perlman described to the court the aftermath of a Palestinian suicide bombing that targeted a crowded bus in Jerusalem.
"Bodies, corpses were flying. They were flying onto balconies and rooftops. People were severed in two, severed into pieces," the Associated Press quoted the 70-year-old Perlman as saying.
One of the bombers, Wafa Idris, is widely regarded as a hero in the Palestinian territories, as are other militants who have carried out attacks, the AP reported.
The 2004 lawsuit was brought under the Anti-terrorism Act of 1991 and seeks $1 billion from the PA and the PLO. Lawyers for the plaintiffs say any damages awarded would be automatically tripled because the claims involve acts of terrorism.
Officials in cash-strapped Palestine are worried about a potentially hefty bill, as well as damage to its international image.
The Palestinians recently moved to join the International Criminal Court at The Hague, where they hope to pursue war crimes charges against Israel, and a negative verdict could be a setback to those goals.