his apartment, an aide said. Police then escorted Kadhafi's former special envoy to the public prosecutor's office.
Reached on his mobile telephone, he sought to play down the arrest, however, and said he would file a complaint with the Egyptian public prosecutor and Libyan authorities.
"I am on my way now, in the company of lawyers," he said before arriving at the prosecutor's office.
A Libyan embassy official told AFP Qaddaf al-Dam had surrendered after the consul met him in his apartment and told him "there is no escape". His bodyguards were Libyan and Palestinian, the official said.
A security official and state television said Qaddaf al-Dam gave himself up to police after they besieged his home. The official MENA news agency said he would be handed over to the Libyan authorities, who want to put him on trial.
Another official at the Libyan embassy told AFP the authorities had also arrested two other figures, former Libyan ambassador Ali Maria and Mohammed Ibrahim, the brother of senior Kadhafi-era Libyan official Ahmed Ibrahim.
"This is part of a plan by the Libyan authorities in coordination with Egyptian authorities to arrest wanted Libyans living in Egypt," Abdel Hamid al-Safi said.
It was not immediately clear whether Qaddaf al-Dam, whose mother was Egyptian, carried Egyptian nationality, which could complicate his transfer to Libya to stand trial.
A Libyan embassy official said he was certain Qaddaf al-Dam was not an Egyptian citizen before the 2011 uprising that toppled Kadhafi. But his nephew said he carried with him an Egyptian national identity card.
Shortly after the start of the uprising, Qaddaf al-Dam had announced he had resigned from all official functions.
Until then, Qaddaf al-Dam, who had permanent residence in Cairo, oversaw Libya's relations with Egypt.
Residents of Zamalek said they had heard gunfire overnight.
Qaddaf al-Dam's nephew and aide said that "masked men" had tried to storm the apartment at 2:00 am.
"His bodyguards fired at them and there was an exchange of fire," he said from the prosecutor's office where Qaddaf al-Dam was being questioned. The nephew requested anonymity for fear of reprisals.
Speaking to French satellite channel France 24, Qaddaf al-Dam said several people had been injured during the shooting.