Rupert Murdoch and his son James agreed to appear next week before UK lawmakers investigating whether News Corp. employees hacked the cell-phone messages of private citizens and government officials.

Rupert Murdoch, CEO and chairman of News Corp., and James, the company’s deputy chief operating officer, are scheduled to appear Tuesday before Britain’s Parliament to answer questions about the controversy, which led News Corp. to shutter its News of the World.

In his first public comments on the controversy, Rupert Murdoch defended the company’s handling of the crisis and said News Corp. would set up an independent committee to “investigate every charge of improper conduct.” News Corp. owns The Post.

Both Murdochs initially said they were unable to appear at the inquiry due to conflicts. After receiving formal summonses from Parliament to appear, both executives agreed to appear at the inquiry. Rebekah Brooks, who heads News Corp.’s UK newspaper division, earlier agreed to testify and will appear with the Murdochs.

Meanwhile, the FBI is said to be investigating claims by two US lawmakers that victims of 9/11 may have been targets of hacking by News Corp. employees, Bloomberg News reported.

The FBI said it was reviewing letters from New York Reps. Peter King, a Republican, and Louise Slaughter, a Democrat, demanding a probe into whether hacking involved US citizens. The Justice Department had no comment.