Rebel commanders said the fighting centered on Bir al-Ghanam, a strategic point on the road to the Libyan capital.
Meanwhile, the African Union panel on Libya meeting in the South African capital Pretoria said Kadhafi would not participate in peace talks, in what appeared to be a concession.
The panel "welcomes Colonel Kadhafi's acceptance of not being part of the negotiations process," AU peace and security commissioner Ramtane Lamamra said, reading a prepared statement issued after four hours of talks.
A South African official who requested anonymity said after the panel meeting: "We wanted Kadhafi to make a public statement that he would not take part in the negotiations but he would not."
Asked about the significance of his refusal to make a statement, the official, part of the South African team that travelled to Tripoli last month in a failed bid to launch peace talks, said: "This means he is finished."
On Saturday, Abdel Hafiz Ghoga, vice chairman of the National Transitional Council (NTC), said that they had been in touch with loyalists over the possibility of Kadhafi submitting to internal exile.
French Foreign Minister Alain Juppe said Sunday there had been contact between the two camps that specifically involved the fate of Kadhafi.
"I know that they covered, for example, the fate reserved for Kadhafi himself, which is one of the central questions today...," he told France's RTL radio.
But Kadhafi government spokesman Mussa Ibrahim said Sunday the leader had no intention of quitting power.
"Kadhafi is here. He is staying. He is leading the country. He will not leave. He will not step down because he does not have any official position," Ibrahim said.
"We will not give in to some criminal gangs who took our cities hostage. We will not give in to the criminal organisation of NATO. Everyone continues to fight. We are ready to fight street to street, house to house," he added.
The wording of the AU panel's statement was far softer than South African President Jacob Zuma's opening remarks. He had again warned NATO against overstepping the mandate of the UN resolution imposing a no-fly zone over Libya.
"The intention was not to authorise a campaign for regime change or political assassination," Zuma said behind closed doors, according to a text of the speech.
Zuma urged both Kadhafi and the rebel NTC to make compromises to reach a deal in the face of a conflict that was degenerating into a protracted and bloody deadlock.
"On the ground, there is a military stalemate which cannot and must not be allowed to drag on and on -- both because of its horrendous cost in civilian lives and the potential it has to destabilise the entire sub-region," he said.
Jean Ping, head of the African Union Commission, its executive body, also underlined the regional effect of the conflict in his speech.
"The Libyan conflict ... is entering its fifth month, with its lot of suffering and its toll, each day heavier, in human life...," he said, according to text received by AFP..
"Tens of thousands of migrant African workers have had to return to their countries of origin...," he added.
"Hundreds of them have perished at sea, trying desperately to flee the fighting and other military operations."
News of the spread of weapons in Libya only reinforced fears of regional instability, he added, making a political solution all the more urgent.
The AU has been leading mediation efforts in Libya with the support of other key players including Russia.
As well as Zuma, Sunday's meeting was attended by other African presidents, Amadou Toumani Toure of Mali, Mohamed Ould Abdel Aziz of Mauritania and Yoweri Museveni of Uganda, as well as Congo Foreign Minister Basile Ikouebe.
They are to report back to a full summit of the African Union, of which Libya is a member, in Equatorial Guinea from Thursday.
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