The leaders of Sudan, Chad, Congo Republic, which heads the 53-nation African Union, and Burkina Faso, which chairs the Sub-Sahara Sahel African grouping, will join al-Qadhafi in the meeting on Wednesday.
Sudan and Chad are members of the Sahel grouping.
Foreign ministers of the five countries met on Monday to prepare for the summit, the officials added.
Libyan Foreign Minister Mohammed Abdul Rahman Shalgam told the meeting: "We are meeting today to go beyond the tension between Chad and Sudan and reach practical solutions to overcome the negative issues between the two countries."
He said the summit on Wednesday "aims at strengthening the links and overcoming the tensions".
Chad and Sudan, whose leaders both have good relations with al-Qadhafi, accuse each other of backing insurgents fighting the governments in N'Djamena and Khartoum.
Chad accuses Sudan of supporting insurgents sworn to oust President Idriss Deby and who attacked the Chadian border town of Adre in December.
Chad then declared a "state of belligerence" with its eastern neighbour.
Abdul Rahman Shalgam: We are
meeting to reach solutions
Chad says the insurgents attacked Adre from Darfur and the Chadian insurgents admit to having had training camps there in the past.
Tribes span both sides of the border and Deby himself took power in a coup he launched from Darfur in 1990.
Human Rights Watch said on Sunday tens of thousands of people were now displaced within Chad because of attacks by Sudanese and Chadian militias based in Darfur, sometimes with apparent Sudanese backing including helicopter gunships.
The New York-based group said the Chad side of the border had become more vulnerable following the attack on Adre.
Sudan's state minister for foreign affairs Al-Samani Al-Wasiyla said the rights group often came up with "stories based on third- or fourth-hand information".
He told reporters in Khartoum that Sudan was disarming those Chadian insurgents they found and had attacked others who refused to lay down their weapons.
He said technical committees were working in Tripoli to prepare the mini-summit. It was not clear whether it would take place in the capital or in Sirte, Gaddafi's home town.
Diplomats said they were sceptical about what Libya might achieve at the summit after other African leaders made little progress on the issue.