In a 30-page opinion, Judge George B. Daniels of the Southern District of New York ruled that federal courts lacked legal jurisdiction to seize the funds. He also said that awarding them to the families would be unconstitutional because it would mean effectively recognizing the militants as the legitimate government of Afghanistan.

The Sept. 11 families and insurance companies “are entitled to collect on their default judgments and be made whole for the worst terrorist attack in our nation’s history, but they cannot do so with the funds of the central bank of Afghanistan,” Judge Daniels wrote.

The ruling by Judge Daniels adopted the recommendation of a magistrate judge, Sarah Netburn, who analyzed the matter in a report last August that also found that the families were not entitled to the funds. But it left the decision to him.

Judge Daniels’s opinion was the first definitive ruling in a complex saga at the intersection of foreign policy, international economics, counterterrorism and domestic politics, a situation arising from a country being seized by a terrorist organization and left without a government that is recognized as legitimate.

“This decision deprives over 10,000 members of the 9/11 community of their right to collect compensation from the Taliban, a terrorist group which was found liable for the 9/11 attacks on America,” Mr. Wolosky said.

When the government of Afghanistan collapsed as the Taliban took over in August 2021, there was about $7 billion in Afghan central bank funds deposited at the Federal Reserve Bank of New York. A group of Sept. 11 families that years earlier had sued the Taliban for their losses, winning a default judgment when the militants failed to show up in court, then moved to seize the funds to pay off the judgment debt.

Last February, President Biden froze the funds, reserving about half to be spent on helping the Afghan people while leaving the remaining $3.5 billion for the families to keep going after in court.

It is not clear what will happen to the $3.5 billion the president set aside for the families to keep pursuing if their appeals ultimately fail. One possibility is that Mr. Biden or a successor could use executive power to add it to the half he set aside for Afghans and which is now controlled by a special fund in Switzerland.

The effort by the initial group of Sept. 11 families — known as the Havlish plaintiffs and represented by Mr. Wolosky’s law firm — to seize the money was disputed for several reasons.

Other plaintiff groups of Sept. 11 families sought an equal share in any proceeds, but under New York law the Havlish group, made up of about 150 people linked to 47 estates from the nearly 3,000 people killed, could get paid in full first. Ultimately, the Havlish group negotiated a deal with other groups in which they would receive a lesser share in exchange for their support.

Another faction of relatives, however, joined exiled Afghans, among others, in urging the court to reject giving any of the money to Sept. 11 families. It belonged to the Afghan people, they argued, and should go toward helping them during a humanitarian crisis caused by the collapse of the country’s economy.

Agreeing with Judge Netburn’s earlier report and recommendation, Judge Daniels expressed sympathy for both the families and the people of Afghanistan suffering anew at the hands of the Taliban. But he said the law precluded the court from awarding any of the Afghan central bank funds to the Sept. 11 plaintiffs to pay the Taliban’s debts.

For one thing, he wrote, because the Afghan central bank — known as Da Afghanistan Bank, or DAB — is an instrument of a foreign state, American courts lack jurisdiction to seize its property under the Foreign Sovereign Immunities Act.

While another law called the Terrorism Risk Insurance Act can make an exception to that rule when there is a judgment against a state sponsor of terrorism, he wrote, the Sept. 11 families hold judgments against the Taliban, not the sovereign nation of Afghanistan. Moreover, he noted, Afghanistan has never been designated a state sponsor of terrorism.

Even if he was wrong about that and the court did have jurisdiction over the bank and its assets, Judge Daniels wrote, the Constitution prevented him from making the necessary finding that the bank is an “agency or instrumentality” of the Taliban.

“Finding that the Taliban controls DAB or can use DAB to advance its goals implies that the Taliban is Afghanistan’s government,” he wrote. “The Constitution vests this authority to recognize governments in the executive branch alone.”