CAIRO, March 26 (Reuters) - Egypt extradited two members of the regime of ousted leader Muammar Gaddafi to Libya on Tuesday but did not hand over a third for reasons including his claim to Egyptian citizenship, officials said.

Ali Maria, Gaddafi's last ambassador to Cairo, and Mohamed Ibrahim Mansour, the head of a Libyan state fund, were arrested in Cairo last week. They were put on a private plane to Libya on Tuesday morning, airport officials said.

The third Libyan was Ahmed Gaddaf Alddam - a cousin of Gaddafi. He claims that both his both his father and mother were Egyptian citizens and is suing the government so he can obtain proof of his nationality, Al Gomhuria newspaper reported.

Gaddaf Alddam is also being investigated in Egypt on accusations he attacked Egyptian police during his arrest, said Kamel Girgis, the head of the international cooperation unit in the prosecutor general's office.

Libyan Prime Minister Ali Zeidan had called for the immediate handover of the men.

Libya wants Mansour for fraud and Gaddaf Alddam for counterfeiting, forgery, fraud and money laundering, according to Interpol's website. Maria is also wanted in Libya on charges of financial corruption, an Egyptian judicial source said.

In exchange for the detained Libyans, Egypt had sought the release of four Egyptian Christians held in Libya for a month after being accused by the prosecutor of proselytising, Egyptian judicial sources said last week. A judicial source in Cairo said Libya had pledged to take steps towards their release. (Writing by Tom Perry; Editing by Ruth Pitchford)