NEW YORK (Reuters) - Families of U.S. Marines killed in a 1983 bombing in Lebanon demanded ownership on Monday of a New York skyscraper that U.S. prosecutors say is owned by companies illegally funneling money to Iran.

In a lawsuit filed in New York federal court, the relatives sought the 36-story building at 650 Fifth Avenue in Manhattan as payment for more than $2.6 billion in damages awarded by a U.S. court three years ago.

A U.S. judge in 2007 found Iran's government liable for providing material, financial and logistical support to Hezbollah, the guerrilla group accused of bombing the U.S. Marine barracks in Beirut and killing 241 military personnel.

The damages have not been paid, so the families of those killed and wounded are pursuing the skyscraper.

U.S. prosecutors filed a civil lawsuit in November seeking to revoke the Alavi Foundation and Assa Corp's ownership of 650 Fifth Avenue because they say both companies were sending money to the Iranian government's Bank Melli.

The lawsuit also sought to seize "all other assets" of the two entities, including bank accounts and real estate in New York, Maryland, Virginia, Texas and California, which included some mosques.

The U.S. Treasury has designated the bank as a weapons proliferator and banned U.S. citizens from dealing with it.

(Reporting by Michelle Nichols; Editing by Peter Cooney)