On August 9, 2001, Ahlam Tamimi, a member of Hamas, drove a suicide bomber to the Sbarro restaurant in the heart of Jerusalem, where the bomber blew himself up, killing 15 people including Judy Greenbaum, an American citizen from New Jersey. On March 5, 2003, Abigail Leitel, a 14-year-old Baptist schoolgirl born in New Hampshire, was killed, along with 14 Israelis, by a suicide bomber who exploded a bomb on a Haifa bus.

Three Hamas members — Fadi Muhammad al-Jabaa, Maedh Abu Sharakh, and Majdi Muhammad Amr — plotted that deadly attack. On September 9, 2003, a Hamas suicide bomber slew seven people — including American citizens David, a doctor, and Nava Applebaum, who was his daughter and was to be married on that day — at Café Hillel in Jerusalem. Ibrahim Dar Musa helped plan that bombing.

The perpetrators of each of these murders of Americans violated American criminal law and could be prosecuted in American courts. Yet all of them are now free and living in Jordan or Gaza because Hamas demanded that they be released from Israeli prisons in exchange for Hamas’ release of Gilad Shalit, an Israeli soldier who Hamas captured and held in captivity for more than five years.

Since the Antiterrorism Act of 1990, it has been a capital crime under American law, punishable by “death or imprisonment for any term of years or for life, or both,” to “kill a national of the United States, while such national is outside the United States.” A conspirator in such a crime can get up to 20 years imprisonment. No statute of limitations precludes prosecution of old offenses.

Another law, passed in 1994, made it a federal crime to use an explosive bomb “against a national of the United States while such national is outside of the United States.” In 2002 Congress authorized prosecution in American federal courts of anyone who, with criminal intent, injured “a national of the United States” outside the United States by detonating “an explosive or other legal device in, into or against a place of public use” or “a public transportation system.”

Prosecutions have been brought in American federal courts against individuals responsible for bombings that killed Americans in the Philippines, Colombia, Kenya, and Tanzania. Many of the individuals accused of these crimes were brought here for trial following their extradition, on the request of the United States, from foreign countries. American prosecutors have not, however, charged the Hamas perpetrators of bombings in Israel such as the 2001 and 2003 bombings in Jerusalem and Haifa, even though American citizens were murdered in these attacks. They have relied on the Israeli legal process to arrest and punish the perpetrators.

Tamimi, al-Jabaa, Sharakh, Amr, and Dar Musa were prosecuted and convicted in Israeli courts. They and other perpetrators of these murders received either multiple sentences of life imprisonment or long prison terms. Until they were released by Israel’s government under duress in order to bring Gilad Shalit home, they expected to spend the rest of their lives in Israeli prisons. They are now free in Jordan or Gaza.

The Department of Justice should now indict, extradite, and put to trial in United States courts, under American law, these killers of American citizens. Jordan has an extradition treaty with the United States that covers all offenses “punishable under the laws in both Contracting States by deprivation of liberty for a period of more than one year or by a more severe penalty.” A conspiracy to commit such an offense is also covered by Article 2(2) of the treaty.

No provision of any extradition treaty should preclude bringing these criminals to justice in the United States. The Jordan treaty bars extradition for “political offenses,” but it would be hard to claim that the mass terrorist killings of civilians in Jerusalem and Haifa were only “political offenses.” At the least, Jordan should be put to that test.

Nor could Jordan or any other requested country invoke the bar against double jeopardy that appears in many extradition treaties to prevent second punishment after a criminal prosecution for the extraditable offense has been conducted and fully carried out. That provision obviously does not prevent extradition of a fugitive who flees a country where he has been convicted in order to avoid imprisonment. It also should not prevent extradition if, by some other unlawful means such as Hamas’ extortionate demand, the criminal process is aborted.

Congress’ objective in enacting the provisions authorizing prosecution of such crimes in United States courts, even though they were committed elsewhere, was to insure that those who murdered American citizens like Judy Greenbaum, Abigail Leitel, and the Applebaums would not be able to avoid just punishment for their crimes. That goal can now be realized only if the United States Department of Justice takes prompt and effective action.

Mr. Lewin is a Washington lawyer who was a federal prosecutor and served as deputy assistant attorney general in the civil rights division of the U.S. Department of Justice.