The staggering legal bill Iran faces for its involvement in terrorism is mounting, with nearly a third of a billion dollars added to the tab in recent days by a single judge sitting in Washington.

The sum of terrorism-related verdicts returned by American courts against the Iranian government and Iranian leaders stands at about $6 billion, according to court records and congressional reports. The rulings hold Iran responsible for terrorist attacks carried out by militant groups the country has sponsored, including Hamas, Hezbollah, and Palestinian Islamic Jihad.

The most recent financial strike against Iran came on Wednesday, when a federal judge in Washington awarded $12 million in compensatory damages and $300 million in punitive damages to the estate and family of an American, Yonathan Barnea. In 1996, Barnea, 19, was killed in the Hamas-organized bombing of a passenger bus in Jerusalem.

Under prevailing law, foreign governments are immune from punitive damages, so the $300 million award was directed specifically at Iran’s “supreme leader,” Ayatollah Ali Khamenei.

While the $300 million figure may be eye-popping, it is far from unusual in cases involving Iranian-sponsored terrorism. More than a dozen other lawsuits against Iran have resulted in similar awards that were calculated by taking the Iranian government’s estimated $100 million annual expenditure on terrorism and multiplying it by three.

Since the cases often involve multiple victims of the same terrorist incidents, one judge, Royce Lamberth, has overseen many of them. Last week, he awarded $2.5 million to the sister of an American serviceman killed in Hezbollah’s bombing of the American Embassy compound in Beirut in 1983. Earlier in March, Judge Lamberth ordered Iran to pay $11 million to Seth Ben Haim, an American badly wounded in Palestinian Islamic Jihad’s attack on a bus in Gaza in 1995.

“It’s snowing judgments against Iran,” a New Jersey man who helped to blaze the trail for such lawsuits, Stephen Flatow, told The New York Sun. Mr. Flatow’s daughter, Alisa, was killed in the same bus attack that gravely injured Mr. Ben Haim.

Congress opened the door to anti-terror litigation in 1996 by passing a measure stripping sovereign immunity from countries on the State Department’s list of state sponsors of terrorism. Later that year, Mr. Flatow led a successful effort to allow punitive damage awards in terrorism cases involving foreign officials and government agencies.

Despite the blizzard of verdicts against Iran, the victims of terrorism and their attorneys have had difficulty recovering Iranian funds and property. Nearly all trade between America and Iran has been banned since the hostage taking at the American Embassy in Tehran in 1979. As a result, there are few Iranian assets within the reach of the American courts.

One lawyer frustrated with the lack of progress in satisfying the verdicts, David Strachman, has taken a new tack, attempting to seize Persian antiquities in the collections of American museums and research institutions.

Mr. Strachman represents five Americans who brought suit against Iran over a Hamas-led bombing on Jerusalem’s Ben-Yehuda Street pedestrian mall in 1997. In 2003, a federal judge in Washington ordered Iranian agencies and officials to pay $97 million to the five plaintiffs, who suffered injuries in the bombing. As in the other cases, the Iranian defendants never showed up to contest the lawsuit.

In 2004, the University of Chicago’s Oriental Institute announced it was going to return to Iran 300 ancient tablets loaned to the university in 1937. A university press release described the repatriation as part of an effort to set up a “partnership” with Iranian cultural officials.

Mr. Strachman caught wind of the impending return and swooped in, filing court papers to take possession of the artifacts, as well as other Persian treasures at the Field Museum.

In December, a federal magistrate, Martin Ashman, ruled that neither the university nor the museum had standing to block the seizure of the Iranian property. He said Iran could object, but noted it has not made any effort to appear in the case.

Lawyers for the museum and the university have asked a judge to overturn the magistrate’s ruling and warned of dark consequences if it is not. “American national treasures that are currently on loan to foreign museums are jeopardized by this opinion, as is the whole orderly process of deference to a legislatively enshrined respect for sovereign power,” the attorneys argued. “Iran is entitled to the same treatment under the law as our nation’s closest allies.”

The Justice Department has also stepped into the dispute. In a brief filed last month, government lawyers complained that permitting the seizure “denies to a foreign sovereign the ‘grace and comity’ to which it is ordinarily entitled.”

The Justice Department said it was not “defending Iran’s behavior,” but the brief warned that America could end up on the hook at an international tribunal if the artifacts are seized. “Iran may intend to seek compensation from the United States, and ultimately from U.S. taxpayers, in those proceedings if the artifacts are improperly allowed to be attached here,” the brief said.

Mr. Strachman said he was taken aback by the government’s intervention. “It’s shocking that the U.S. government would file a brief supporting and basically defending Iran on the very same day that the State Department files a report indicating that the Iranian government is the biggest threat to world peace and specifically to U.S. national security,” he said in an interview.

He referred to the warnings about American collections being seized abroad as “a straw man.” “That’s never happened,” the lawyer said.

Mr. Strachman has also moved to seize Persian artifacts from Harvard University and the Museum of Fine Arts in Boston. A judge is scheduled to hear arguments on that matter next month.

While the scramble over Iranian assets goes on, Congress has allowed the plaintiffs in 16 terror-related cases to be paid out of the American treasury. Laws passed in 2000 and 2002 allowed payments totaling approximately $400 million to those plaintiffs. The sum corresponds to an amount the late Shah of Iran’s government left in American military sales accounts.

Mr. Flatow said it would be better to get the money from Iran directly, but he defended the government payments as similar to the compensation paid to victims of the September 11, 2001 attacks on the World Trade Center. He said two bills pending in Congress would make it easier to collect the awards from Iran.

The largest amount the treasury has paid to the family of a single victim of Iranian-related terrorism was $57 million paid to the kin of an American marine taken hostage and killed while on peacekeeping duty in Lebanon, Colonel William Higgins. The average federal government compensation to families of those killed at the World Trade Center was $2 million.

A Congressional Research Service report issued last year observed that congressional enactments and a flurry of legal rulings have led to significant disparities in the amounts terror victims have been able to collect.

“The compensation of victims of terrorism who have brought suit, or will bring suit, under the terrorist state exception … seems likely to continue in an ad hoc fashion, with substantial benefits for some and little or none for others,” the report concluded.