"We can confirm that there is a letter, obviously not the first," White House spokesman Jay Carney told reporters aboard Air Force One as Mr Obama flew to an event in Philadelphia.

Mr Carney said Mr Obama had made clear several weeks ago a ceasefire in Libya would be dependent on "actions not words, and a cessation of violence".

"Words are different than actions," he said.

In the letter, Mr Gaddafi said: "This country had already been subjected to embargo and sanctions, furthermore it also suffered a direct military armed aggression during Reagan's time.

"This country is Libya. Hence, to serving world peace ... friendship between our peoples ... and for the sake of economic, and security cooperation against terror, you are in a position to keep NATO off the Libyan affair for good.

"As you know too well, democracy and building of civil society cannot be achieved by means of missiles and aircraft, or by backing armed members of Al Qaeda in Benghazi."

The news comes as forces loyal to Mr Gaddafi shelled Misrata and rebels called for tougher NATO action.

Loud explosions rocked the besieged city, but Libyan officials deny attacking civilians, saying they are fighting armed gangs linked to Al Qaeda.

Accounts from Misrata cannot be independently verified as Libyan authorities are not allowing journalists to report freely from there.

Earlier, official Libyan news agency JANA said Mr Gaddafi sent the letter to Mr Obama following the withdrawal of US war planes from frontline missions in the coalition air operation over Libya.

"The leader of the revolution [Gaddafi] sent on Wednesday a message to US president Barack Obama after the United States withdrew from the aggressive, colonialist coalition crusading against Libya," said the agency, without specifying the contents of the missive.