Libya's internationally recognised Prime Minister Abdullah al-Thani said Wednesday he was ready to talk to militias who control most of his country if "all sides" made concessions.
Thani's government took refuge in the remote eastern town of of Tobruk in August after Islamist-led militia seized the capital Tripoli and then set up a rival administration.
"We open the doors of dialogue with our brothers on the condition that there be concessions from all sides," he told reporters at Khartoum airport as he ended a three-day visit to Sudan.
He did not spell out what concessions he expected to be made.
Thani and his delegation were in Khartoum for talks with President Omar al-Bashir and senior officials.
His government accused Khartoum last month of supporting its militia foes after a planeload of weapons touched down in the southern town of Kufra, allegedly bound for militiamen in Tripoli.
Sudan denied the allegation.
Thani played down the spat on Wednesday, saying it was like a "passing summer cloud" and telling reporters: "Khartoum will host a meeting of the neighbouring countries of Libya, which will be the basis of the dialogue plan."
Bashir said the Libyan delegation's visit had restored relations "to their normal position," adding that Sudan was "interested in bringing peace to Libya".
Bashir said that Khartoum was training hundreds of Libyan military officer because of "the importance of building a strong Libyan national army".
On Tuesday, Foreign Minister Ali Karti said Thani had accepted Sudan's proposal to bring together rival groups in Libya for talks on ending the fighting.
Since a NATO-backed 2011 uprising toppled veteran dictator Muammar Gaddafi, Libya's central authorities have struggled to impose their authority across the vast, mostly desert nation.
Rebel groups who fought Gaddafi have largely refused to give up their weapons, and the government has failed to establish an effective regular army or police force.
During the uprising, Sudan supplied rebels fighting Gaddafi with weapons.