Prosecutors argue the testimony about the human toll of the attacks could be key in deciding whether plotters would face the death penalty if they are eventually convicted.
One of the proposed witnesses, Gordon Haberman, 65, told CNN he "applauded" the prosecution's efforts to expedite the testimony.
"The trials might go on for a number of years," said Haberman, whose only daughter, Andrea, 25, was killed in the attack on the World Trade Center. "They (family members) need to get some statements on record in case they can't make it."
"We're going on 15 years now," he added. "I think the American people deserve a conclusion."
According to the prosecution's motion, the oldest witness is Lee Hanson, 83, whose son, daughter in-law and granddaughter were killed aboard United Airlines Flight #175 when it crashed into the South Tower of the World Trade Center. The youngest proposed witness is 65.
The case against Khalid Sheikh Mohammed and his alleged co-conspirators has already gone on for four years, with the military tribunal's pre-trial proceedings having begun in 2012. In the documents, the prosecution noted a statement made by the defense lawyers that the pre-trial phase could last a decade. The trial is due to take place in Guantanamo Bay but no date has been set.
Prosecutors asked the judge overseeing the trial, Army Col. James Pohl, to allow the depositions of 10 family members to take place in court in October due to the "exceptional circumstances" of their health and age.
"It is impossible to predict the life expectancy of any witness," they wrote, adding that their depositions would provide critical evidence in helping the military commission's possible sentencing decision.
"Evidence about the victim and about the impact of the murder on the victim's family and friends is relevant to the Commission Members' decision as to whether or not the death penalty should be imposed in this case," the 15-page legal motion said.
The prosecution argued for the depositions at a hearing last week where Pohl and the defense questioned why they needed to be conducted in open court, according to The Miami Herald
Another potential witnesses is David Beamer, 74. Beamer's son, Todd, was a passenger on United Airlines Flight #93 who said "Let's roll" before attempting to retake the plane from the hijackers.
The lawyers representing Mohammed and several other alleged conspirators are opposing the prosecution's request, saying in a court filing that "depositions in advance of trial are unduly prejudicial to the defendants" and calling for the commission to deny the prosecution's request.
The defense disputed the prosecutions' rationale for the depositions, arguing that the age of the witnesses was not adequate justification, noting that "at least four of the defense attorneys" were also over the age of 65.