The families, comprising more than 10,000 people, had asked U.S. District Judge George Daniels in Manhattan to put his Feb. 21 decision on hold while they appeal.
"An important public interest lies in the enforcement of terrorism judgments," Daniels wrote.
In ruling against the families, Daniels said awarding them the frozen assets would effectively recognize the Taliban as Afghanistan's legitimate government, which the Biden administration has not done.
The president ordered $3.5 billion set aside to benefit the Afghan people, leaving the rest for the families to pursue.
The case is In re Terrorist Attacks on Sept. 11, 2001, U.S. District Court, Southern District of New York, No.