Shurat Hadin announced the move a day before the Palestinians officially become members of the International Crime Court, where they hope to see Israeli officials prosecuted for similar offences.
"We can't sit idly by. We need to fight back," said Nitsana Darshan-Leitner, the director of the non-governmental organisation.
She alleged that "the Palestinians committed war crimes," and stressed that courts other than the ICC had "the authority to try them, including in the United States".
The 26 US citizens, some of whom also hold Israeli passports, asked that Hamas leaders be prosecuted for firing rockets at Israel's Ben Gurion airport near Tel Aviv during the 2014 war, when Islamist militants in Gaza fought Israeli forces.
Some of them were among people forced to run for shelter when rockets launched at the airport hit a short distance away, said Shurat Hadin.
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Others were passengers on board a Delta flight from New York that was forced to land in Paris, after US flights were diverted from Israel as a result of the rocket fire.
According to US law, a person can be imprisoned for performing an "act of violence" at an international airport, if the victim is a US citizen, said the NGO.
Shurat Hadin hopes to see Hamas officials including exiled leader Khaled Meshsaal and Gaza movement spokesman Sami Abu Zuhri indicted, as well as members of the group's armed wing.
Israel is not a member of the ICC and cannot file complaints there against Palestinians.
Darshan-Leitner said her group had taken the action to fill the "void" and "fight back" against the Palestinians in the international legal arena.
Last month, a US jury found the Palestinian Authority and Palestine Liberation Organisation liable for six attacks in Jerusalem that killed and injured Americans and ordered them to pay more than $650 million, in a case led by Darshan-Leitner.