"I think that Mr. Kadhafi knows what he must do, there needs to be a ceasefire, his forces need to withdraw from the cities that they have forcibly taken at great violence and human cost.
"The sooner that occurs and the bloodshed ends, the better it will be for everyone," the chief US diplomat said.
Speaking alongside visiting Italian Foreign Minister Franco Frattini, she added: "There needs to be a decision made about his departure from power and as (the) foreign minister said his departure from Libya."
The official Libyan news agency JANA said Kadhafi sent the letter following the withdrawal of US war planes from frontline coalition missions in Libya.
"We can confirm that there is a letter, obviously not the first," White House spokesman Jay Carney said, without elaborating on its contents.
Carney said Obama had made clear several weeks ago that a ceasefire in Libya would be dependent on "actions not words, (and) a cessation of violence."
"Words are different than actions," he said.
Clinton said meanwhile that Washington was awaiting a report from Chris Stevens, the US envoy to the Libyan opposition who was dispatched Tuesday to Benghazi in rebel-held eastern Libya.
"He's obviously doing an assessment right now," she added.
Frattini said "the US needs to know more" about the opposition before it follows the lead of France, Qatar and Italy in recognizing Libya's Transitional National Council.
Clinton said the United States "think NATO is performing very well" now that it has assumed command of the military operations against Kadhafi's forces that were launched by US, French and British forces on March 19.
She said it is hard for "air power alone to be sufficient to take out those forces" Kadhafi has deployed, forces she said slip into cities, dispatch snipers onto rooftops and "put so many lives at risk."
"Given the mission that NATO is performing, it is performing admirably," Clinton said.
What she and her Italian counterpart discussed "is how we can... do more to help the opposition make very fast progress," Clinton said.
"What NATO is doing is buying time, buying space, but ultimately we believe that Kadhafi must go, he has lost legitimacy."
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