"It was a good beginning for the important Darfur summit," Egyptian presidential spokesman Suleiman Awad later told reporters.
Beshir and Afeworki have been at loggerheads since the mid-1990s when Sudan and Eritrea accused each other of supporting rebels fighting to topple their governments, severing diplomatic ties over the charges.
Arab diplomats in Tripoli say Kadhafi and Egyptian President Hosni Mubarak have been quietly working behind the scenes for sometime to narrow differences between the two leaders.
The Libyan leader even invited Afeworki to attend the six-way African summit on Darfur.
Egypt admitted that good relations between Sudan and Eritrea would improve the chances of a negotiated settlement to the conflict in Darfur, as Eritrea enjoys good relations with the main rebel groups in the region.
"We hope that the meeting (four-way summit) will be a good opening for the success of the Darfur summit," Awad said.
In addition to its good ties with the Darfur rebel groups, Eritrea hosts the two main rebel movements fighting Sudanese forces in eastern Sudan.
Awad said he hoped Afeworki's participation at the Darfur summit would lead to the achievement of peace in western and eastern Sudan.