WASHINGTON — A fight is breaking out among lawyers for different groups of victims of the Sept. 11, 2001, terrorist attacks over who can try to seize $7 billion in Afghan central bank funds deposited at the New York Federal Reserve — money the Taliban now claims is theirs.

The dispute stems from various lawsuits that groups of attack victims — the estates of those killed, along with their spouses, children and other relatives, and survivors who were injured — filed against Al Qaeda and others they said provided support to the terrorists, like the Taliban. When the defendants did not show up in court, the plaintiffs won default judgments years ago.

Because there was no way to collect money from such defendants, the judgments that they were liable for the losses the plaintiffs had suffered seemed merely symbolic. But the collapse of the government of Afghanistan and the Taliban’s military takeover of that country have raised the possibility that they could seize the Afghan government funds in New York.

This week, after The New York Times reported on such efforts by a group of about 150 relatives of Sept. 11 victims in a case known as Havlish, lawyers for other groups of Sept. 11 victims indicated they want to seek a share of the funds, too. Testiness between the legal teams is rising, letters filed in court show.

The interjections add further complications to a thorny issue that has raised a set of legal and diplomatic problems surrounding the Afghan money in New York, which had accumulated from foreign aid meant for the country’s former government and other sources.

After that government dissolved amid the Taliban takeover, the Federal Reserve blocked access to the account. It was not clear who had the legal authority to gain access to those funds anymore, and longstanding counterterrorism sanctions make it illegal to wire money to the Taliban, who have proclaimed themselves the new government and demanded access to the funds.

In September, the Havlish plaintiffs persuaded a judge to approve sending a U.S. marshal to serve the legal department of the Federal Reserve of New York with a “writ of execution” to seize the money to cover a judgment of roughly $7 billion in damages they obtained a decade ago. Seven State Department contractors who had separately sued the Taliban over a 2016 bombing also sought to enforce a $138 million default judgment.

The Biden administration intervened and said it wanted to inform the court what would serve the interests of the country. The government had been set to tell the court its position on Friday. But this week, the Justice Department asked for a further delay until Jan. 28, saying the administration needed more time.

On Thursday, a federal magistrate judge, Sarah Netburn, granted that delay, writing that “the court recognizes that the treatment of the Afghan funds currently in the Federal Reserve Bank of New York involves numerous complicated questions of law and policy.”

Lawyers in the Havlish case have been negotiating with the Biden administration over a potential deal in which they would redirect some of the funds to humanitarian assistance in Afghanistan if the government backs their claim. They also offered to give some to certain other spouses and children of Sept. 11 victims who, for technical reasons, did not receive payments from a compensation fund for victims of terrorism set up by Congress.

But under their proposal, plaintiffs in other Sept. 11 lawsuits — several of which cover larger numbers of victims — would not receive payouts from the Afghan account.

The Havlish plaintiffs appear to be the only major group of Sept. 11 plaintiffs who already have a judgment saying the Taliban owe them money. Several people familiar with the cases said that was because all of the defendants named in the Havlish lawsuit defaulted. The other cases named a few defendants who showed up in court, delaying the damages stage even for those declared liable by default.

The government’s request for the delay brought to the surface growing tensions.

Timothy B. Fleming, a lawyer in the Havlish case, had told the court that the delay the government was seeking would be too long and that it should get at most until Dec. 28.

But on Wednesday, Andrew J. Maloney, a lawyer for plaintiffs in a different Sept. 11 victims case known as Ashton, wrote the court and expressed support for the government’s request for a delay until Jan. 28. He said the delay would give his clients time to obtain a damages award against the Taliban and to formally name additional plaintiffs to the case.

“We think all 9/11 defendants should be treated the same and most everybody, if not all, have default judgments against the Taliban,” he said in an interview. “We want to have that money divided proportionately among all the 9/11 death cases and not just a small group.”

Mr. Fleming wrote back to the court earlier on Thursday portraying the Ashton plaintiffs’ opinion about the requested delay as irrelevant since “by their own admission” they do not currently have an enforceable damages judgment against the Taliban.

“The court should disregard the suggestions and speculations of non-parties about how to manage this proceeding,” he wrote. “If the Ashton plaintiffs ever do obtain final, enforceable judgments against the Taliban, the Havlish plaintiffs will be prepared to address the priority of those claims at that time.”

A New York law suggests that even if the other plaintiffs obtain damages judgments and file claims too, the Havlish plaintiffs can argue that because they filed theirs first, they are entitled be paid off first. Their judgment debt is roughly equal to all the assets in the account.

Lawyers for another major Sept. 11 lawsuit that involved a 2006 default liability judgment against the Taliban, known as the Burnett case, are also planning to seek a share of the Afghan central bank proceeds, if those funds are going to be distributed for that purpose, according to a person familiar with that case.

Also on Thursday, Jerry S. Goldman, a lawyer in yet another Sept. 11 lawsuit, known as O’Neill, wrote the court to urge delaying matters until late January. He said the additional time would keep the funds “fully secured” while the Biden administration and the court sort through competing claims.

The O’Neill case, filed in 2004, does not name the Taliban or Afghanistan as defendants. But Mr. Goldman said in an interview that his clients deserved a fair share, too.

“I think everybody needs to be treated equally,” he said, adding, “The funds should go to all of the victims, not a select few.”