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Secretary of State Hillary Rodham Clinton said Sunday she supports calls for a U.N. probe into the death of Libyan leader Muammar al-Qaddafi, whose being shot point-blank in the head has given rise to concerns he was executed last week rather than killed in crossfire.

"Let's have an investigation, I fully support the United Nations investigation and I fully support the Transitional National Council's own call for an investigation," said Clinton, referring to Libya's new leadership, which on Sunday was declaring the country liberated and beginning the process of forming a new government.

Qaddafi was captured wounded, but alive Thursday in his hometown of Sirte. Bloody images of Qaddafi being taunted and beaten by his captors have raised questions about whether he was killed in the fighting between his military and rebel fighters or whether he was taken out during a dispute over who would hold him in custody.

Clinton told "Fox News Sunday" that she supports an investigation "on the merits" and because it will help in a challenging transition process that will lead to reconciliation, which includes reconciliation with former regime supporters who "don't have blood on their hand."

"Such an investigation would be very important for accountability, rule of law and pave the way to the inclusive democratic future that the Libyans tell me they want," she said.

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Clinton also said that President Obama has been a "smart" leader in his handling of international upheavals.

"He was the one who put together a coalition that eventually removed Qaddafi, so I think it's important that in this very complex, dangerous world we have somebody in the White House who understands that America has to lead, and leadership is essential, but we have to look at every situation and make the right decision," she said.