US officials met with their Libyan counterparts to deliver the ultimatum "Muammar Qadaffi must go," the Associated Press reports.
The secret meeting occurred over the weekend as Libyan government forces fought rebels for control of the oil port of Brega, which reble fighters said Monday they now had surrounded. Tripoli has denied the report.
The meeting was held "to deliver a clear and firm message that the only way to move forward is for Gaddafi to step down," a US State Department official said.
"This was not a negotiation. It was the delivery of a message." The official said no more meetings were planned.
Libyan officials responded to the report saying they welcomed discussions but only without preconditions.
"Any dialogue with the French, Americans, British is welcome," government spokesman Ibrahim Moussa told journalists in Tripoli. "We will discuss everything, but do not condition your peace talks. Let Libyans decide their future."
Moussa said the meeting was in Tunisia on Saturday. The US official said it followed repeated contacts from the Libyan leader's emissaries.
Russia has criticized the United States and others for recognizing the rebel leadership as the legitimate government of Libya, saying they were taking sides. Russia has not explained the virtue of neutrality over taking sides, however.
US Secretary of State Hillary Clinton announced US recognition of the rebels on Friday, a major diplomatic step that could unblock billions of dollars in frozen Libyan funds.
Qadaffi is refusing to step down despite the rebellion, NATO air strikes and defections of members of his inner circle.
On Saturday -- as his envoys met US officials -- he called rebels traitors and said he had no plans to leave the country.