Talks between South African's president and Libyan leader Muammar Gaddafi in Tripoli have ended with no announcement towards an end to Libya's conflict.
Jacob Zuma said Col Gaddafi would agree to a ceasefire but would not step down, as demanded by Nato and Libyan rebels.
The ceasefire proposal was rejected last month after a mediation mission by Mr Zuma on behalf of the African Union.
A spokesman for Libya's rebels dismissed calls for a ceasefire, and promised to continue their offensive.
Italy Foreign Minister Franco Frattini is expected to visit the rebel-held city of Benghazi on Tuesday.
Mr Frattini will meet members of the Libya Transitional National Council, the opposition alliance against Gaddafi.
His visit comes a day after a news conference in Rome where eight senior Libyan army officers announced their defection from Col Gaddafi's forces.
On Monday, Nato temporarily lifted its no-fly zone over Libya to allow President Jacob Zuma's South African air force plane to land at the main military air base next to Tripoli.
Mr Zuma emerged from the talks saying Gaddafi is ready to accept an African Union initiative for a ceasefire that would stop all hostilities, including Nato airstrikes in support of rebel forces.
"He is ready to implement the road map," said the South African president.
He added that Nato raids were undermining African mediation efforts.
"We discussed the necessity of giving the Libyan people the opportunity to solve their problem on their own," he added.
But the calls for a ceasefire were immediately rejected by rebel Foreign Minister Fathi Baja, in Benghazi.
"We refuse completely. We don't consider it a political initiative, it is only some stuff that Gaddafi wants to announce to stay in power," he told the Associated Press news agency.
Mr Baja added that the rebels were preparing to launch an offensive against Gaddafi.
The BBC's Andrew North, in Tripoli, said Mr Zuma appears to have made little progress in his attempts to find a peaceful resolution to Libya's crisis.
Both Nato and Libya's rebels had already rejected the AU plan, on the grounds it does not call on Mr Gaddafi to step down.
With the Libyan leader standing firm, it looks like both sides are deadlocked, our correspondent said.
It looks likely that Nato will now intensify its military campaign, with Tripoli already bracing itself for more air strikes, he added.
Fresh air raids on the capital were reported on Monday night, according to Libyan state television.
Nato fighters also targeted sites in the desert city of Al Jufrah, 460km (285 miles) south of Tripoli, it was reported.
The raids have not been confirmed but planes were heard flying over the capital at around midnight local time (2200 GMT Monday), the AFP news agency said.