"We will accompany him to his last resting place and we pray God to give us the courage to continue his work of tolerance and peace for the welfare of Guinea," Toto Camara said at a national stadium packed beyond its 20,000 capacity.
Meanwhile, shots were heard in the capital and suburbs late on Friday after a curfew came into force.
A military source said it was only a question of "dissuasive" firing to encourage people to go home. Al Hassan Sillah, a journalist, told Al Jazeera that the gunfire came from soldiers enforcing the curfew.
Conte's coffin, draped with Guinea's red-yellow-and green flag and escorted by presidential guards, was driven around a stadium as the crowd stood and applauded.
|Camara's takeover of power has been greeted enthusiastically by many Guineans [AFP]
The body was later taken to a mosque and then to the village of Lansanaya, around 120km northwest of Conakry, for burial.
Earlier, the coffin was displayed at a ceremony held in the parliament building.
Among the mourners were the presidents of Guinea's neighbours, Ernest Bai Koroma of Sierra Leone, Liberia's Ellen Johnson Sirleaf, Laurent Gbagbo of Ivory Coast and Joao Bernardo Vieira of Guinea-Bissau.
Jean Ping and Mohammed Ibn Chambas, the heads of the African Union and the Economic Community of West African States, were also present along with civil and military officials, and Conte's wives and children.
Despite frequently denouncing Conte for "pillaging" the country, trade union leaders were among those paying respect with messages of condolence to his family.
Beset by calls from abroad to return the country to civilian rule and stage elections, Moussa Dadis Camara has invited foreign envoys to meet him "to reassure the international community".
He won the allegiance on Thursday of Ahmed Tidiane Souare, the former prime minister, who addressed him as "Mr President" and told Camara that he and his ministers were ready to serve the junta.
Camara, who has already appointed a military-dominated governing council in place of the civilian government, assured Souare of his safety and told him that military rule was only temporary.
The junta, in a statement read on national radio, said it would first hold an "informational meeting" at 1000 GMT on Saturday with "representatives of civil society, political parties, religious faiths and unions".
A second meeting would take place at noon (1200 GMT) for representatives of the UN, the European Union and African Union and the Group of Eight leading industralised countries.
The coup has attracted widespread international criticism, particularly of Camara's decision to rule out elections for at least two years.
In a new statement on Friday, former colonial power France urged Guinea to organise free elections within six months "so that the people of Guinea can freely express its will".