Mustafa Abdul-Jalil told thousands of supporters at a Sunday ceremony that Islamic Sharia law will be the "basic source" of legislation in the country. He also said that existing laws that contradict the teachings of Islam would be nullified.
In a speech that set an Islamist tone for post-Gadhafi Libya, Abdul-Jalil said new banks would be set up to follow the Islamic banking system, which bans charging interest.
However, mounting calls for an investigation into whether Gadhafi was executed in custody overshadowed Libya's "Liberation Day."
U.S. Secretary of State Hillary Rodham Clinton is supporting calls for an investigation into Gadhafi's death. She said it's a vital step for Libya's transition from dictatorship to democracy.
Clinton told NBC's "Meet the Press" that she backs a proposal that the United Nations investigate Gadhafi's death and that Libya's National Transitional Council look into the circumstances, too.
Britain's new Defense Secretary Philip Hammond agreed with Clinton, saying that the Libyan revolutionaries' image had been "a little bit stained" by Gadhafi's death. Hammond added that the new government "will want to get to the bottom of it in a way that rebuilds and cleanses that reputation."
"It's certainly not the way we do things," Hammond told BBC television. "We would have liked to see Col. Gadhafi going on trial to answer for his misdeeds."
Gadhafi was captured wounded, but alive Thursday in his hometown of Sirte, the last city to fall to revolutionary forces. Images of Gadhafi being taunted and beaten by his captors have raised questions about whether he was killed in crossfire as suggested by government officials or deliberately executed.
The 69-year-old's body has been on public display in a commercial freezer in a shopping center in the city of Misrata, which suffered from a bloody siege by regime forces that instilled a hatred for the dictator in Misrata's residents.
People have lined up for days to view the body, which was laid out on a mattress on the freezer floor. The bodies of Gadhafi's son Muatassim and his ex-defense minister Abu Bakr Younis also were put on display, and people wearing surgical masks have filed past, snapping photos of the bodies.
The New York-based group Human Rights Watch, which viewed the bodies, said video footage, photos and other information it obtained "indicate that they might have been executed after being detained."
The vast majority of Libyans seemed unconcerned about the circumstances of the hated leader's death, but rather was relieved the country's ruler of 42 years was gone, clearing the way for a new beginning.
The Associated Press contributed to this report.