London (CNN) -- Saif al-Islam Gadhafi, the son of Libya's deposed leader Moammar Gadhafi, could go on trial "within weeks or months," the country's interior minister said Sunday.
The investigations into the death of Moammar Gadhafi after his capture last year could also be completed soon, Fawzy Abdilal said.
Saif al-Islam's case will be handed to the courts as soon as the prosecutor general completes his investigations, Abdilal told CNN in an exclusive interview.
Separately, military trials of those who "committed criminal acts under the Gadhafi regime" began Sunday in the city of Benghazi, National Transitional Council member Mohammed El Sayah said.
He did not name those who were being tried, but said "even civilians who had guns and fought under the Gadhafi regime" would be tried before military courts.
Trials elsewhere in the country will start later, he said. Benghazi was the center of resistance to the Gadhafi regime last year.
Saif al-Islam Gadhafi, once his father's heir apparent, was captured in November and has been held in the Libyan city of Zintan since then.
Human Rights Watch said after visiting Saif al-Islam in custody last year that he should have a lawyer, but Abdilal implied he had not asked for one.
"He may have a lawyer if he asks for a lawyer," the interior minister said. "Should Saif demand a lawyer, then a lawyer would be provided."
He also brushed aside accusations that authorities are torturing detainees under the new government.
There are "not systematic violations as there were under the Gadhafi regime," he said, even as he conceded that "there may be cases of individuals who take the law into their own hands."
"There is no comparison whatsoever between the situation prevailing under Moammar Gadhafi and the situation now," he said.
Moammar Gadhafi was killed in October, two months after he was deposed by rebel fighters.
Abdilal said the circumstances of his death were complicated.
"It was a battlefield, he was carrying weapons, there were fighters around, no one was controlling those fighters," Abdilal said.
And, he said, "Many people claim that they are the ones who killed Gadhafi, and that is complicating matters."
Abdilal acknowledged that the interim government had not yet succeeded in integrating militias from different cities into a national security force, saying his visit to Britain was partly to seek help with that task.
Fighters from Zintan still control the international airport, he said, adding that he expected them to hand control over to the Ministry of the Interior "within two weeks."
CNN's Raja Razek contributed to this report.