Libyan officials said the talks would focus on ways to end the fighting in Darfur, where the United Nations says around 200,000 people have died and more than 2 million have been made homeless.
The bloodshed in Darfur has spilled into neighbouring Chad in recent months.
In Cairo, presidential spokesman Suleiman Awad said the three leaders would talk about comprehensive reconciliation in Sudan, a solution for Darfur, Arab issues and preparations for an African Union summit in Ghana scheduled for mid-year.
Conflict broke out in Darfur in 2003 when rebel groups took up arms against the Khartoum government, accusing it of neglect. Khartoum says only 9,000 people have lost their lives.
One main rebel group signed a peace agreement with the government in 2006 and small factions later committed themselves to the deal, but it has failed to stop the violence.
An Egyptian official source in Tripoli said the talks would continue discussions Mubarak had had with Sudanese President Omar Hassan al-Bashir on Monday. He did not elaborate.
Deby and Bashir, who have been at loggerheads over military clashes and rebel activity on their countries' volatile border, signed a reconciliation pact in Saudi Arabia on May 3 under the auspices of Saudi King Abdullah.
In the accord, Deby and Bashir echoed previous agreements signed in Tripoli by promising their countries would not be used to harbour, train or fund armed movements opposed to the government of the other.
It was the latest of several bilateral peace accords made by the two leaders over the last 18 months, none of which has prevented fresh violence spilling out of Sudan's conflict-torn Darfur region into neighbouring Chad.
Chad and Sudan have long accused each other of backing rebels hostile to their respective governments.
Past peace deals brokered by Gaddafi have failed to halt rebel movements and raids across the long, porous Darfur border.
- Reuters - Thomson Reuters Foundation
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