More than 80 people were taking part in the talks with Compaoré in a conference hall in the Burkina Faso capital, Ouagadougou, including senior officials of the junta, parliamentary and regional leaders and religious heads.
The talks are aimed at finalising an accord reached last week for a return to civilian rule and ways to end a rebellion that has left the north of the country in the hands of Tuareg separatist and Islamist groups.
Compaoré called on Malians to back the transitional government which is being formed "to strengthen the rule of law, respect republican values and maintain the integrity of the country."
Former parliament speaker Dioncounda Traoré was sworn in on Thursday as interim president after Amadou Toumani Touré resigned under the 6 April agreement.
The 70-year-old mathematician turned politician is expected to name a prime minister soon, and to organise elections within 40 days.
He has threatened "total war" against the northern rebels, who seized a vast swathe of territory amid the disarray that followed the 22 March coup, which the mutineers justified by accusing Touré's government of mishandling the Tuareg rebellion.