Tripoli, Libya (CNN) -- Notions of a cease-fire in Libya quickly faded Saturday as a battle raged for control of the oil town of al-Brega, where rebel fighters claimed they had lost fighters and vehicles to NATO airstrikes.
Airstrikes hit several rebel vehicles and killed at least 13 rebel fighters, spokesmen for the Libyan opposition said Saturday. Seven others were wounded.
NATO was investigating the incident, a spokeswoman said Saturday.
"NATO takes any reports of civilian casualties very seriously, but exact details are hard to verify as we have no reliable sources on the ground," NATO's Oana Lungescu said. "Clearly, if someone fires at one of our aircraft, of course they have the right to defend themselves."
Rebel spokesman Abdul Hafiz Ghoga said opposition fighters had retaken al-Brega after a night of heavy fighting with Moammar Gadhafi's forces.
But it was not immediately clear who commanded control Saturday of the coastal city that has now changed hands six times in as many weeks under the dramatically shifting circumstances of the Libyan war.
Meanwhile, in Misrata, east of Tripoli, two mortars landed at a medical clinic Saturday evening, causing one death and numerous injuries, said a medical official with the city's main hospital.
The doctor, who was not identified for security reasons, told CNN the clinic that was attacked had evacuated patients because of recent attacks, but was being guarded by opposition "fighters and young people."
One person was killed and 15 injured, said the doctor, who was caring for the wounded. Five had serious injuries, including head and chest trauma, he said.
Forces loyal to Gadhafi showed no signs of backing down after officials spurned an opposition cease-fire proposal.
Government spokesman Musa Ibrahim told reporters in Tripoli on Friday that rebels were not "really serious" about the offer, which he said included "silly conditions."
"They are asking us to withdraw from our own cities and open our cities to people, who are holding up arms, who are tribal, violent, no unified leadership, al Qaeda links, and no one knows who they are. If this is not mad, then I don't know what it is," he said. "We will not leave our cities. We will not stop protecting our civilians."
His comments came after Libyan opposition leader Mustafa Abdul Jalil laid out cease-fire conditions that included freedom of expression for the Libyan people and the removal of snipers, mercenaries and militias from western cities.
Ultimately, he said, the opposition's goal remains regime change in Libya.
Ghoga sought to clarify the opposition's position Saturday.
"There is no, and was no, negotiation on a cease-fire with Colonel Gaddafi's dictatorship," he said at a Bengahzi news conference.
He repeated the opposition demands that Gadhafi halt all military action, end the sieges laid on cities like Misrata and allow free speech and assembly.
Sources close to Gadhafi told CNN that political solutions are still possible but that the Libyan leader would relinquish power only to others within his inner circle.
They said there is still time for dialogue but expressed doubts about who would represent the opposition.
Any transition, they said, would involve Gadhafi's second son, Saif al-Islam Gadhafi, and for such a transition to take place there would first have to be an end to the fighting.
The Libyan sources told CNN that for now, Gadhafi remains confident the regime can withstand any challenge from the rebels.
U.S. officials claim Gadhafi's military capabilities have been steadily eroded since the onset of U.N.-sanctioned airstrikes.
The dictator's forces, however, still outnumber rebels by about 10 to 1 in terms of armor and other ground forces, according to Navy Adm. Mike Mullen, the Joint Chiefs of Staff chairman.
CNN's Ben Wedeman, Nic Robertson and Reza Sayah contributed to this report