General Gilbert Diendere made his wish known at talks brokered by West African mediators in the capital Ouagadougou.
The document, signed by the general and exclusively seen by the BBC, says he should remain president until elections – currently due on 11 October, writes BBC online.
BBC West Africa reporter Thomas Fessy says the junta’s proposal is unlikely to signal a return to power of the civilian authorities.
On Saturday one of the mediators, Benin´s President Yayi Boni, had spoken of a breakthrough and hinted at a new transition government.
The mediators hope to reinstate interim President Michel Kafando, who was initially held by the coup leaders. He is now free, whereas the fate of Prime Minister Isaac Zida, who was also detained, is still unknown.
The presidential guard, which supports the coup, remains in control in the capital of the poor Sahelian country.
The overthrow of the civilian interim government – carried out by the presidential guard – was widely condemned. Burkina Faso has been suspended from the African Union.
General Diendere was chief of staff of former President Blaise Compaore, who was deposed in a popular uprising last November.
Mr Compaore is in exile in Ivory Coast and was accused of committing widespread abuses, and trying to change the constitution to extend his term in office.
He had been in power already for 27 years. Some of his key allies has been barred from contesting the up-coming election, BBC notes.
Burkina Faso har været storaftager af dansk udviklingsbistand i et kvart århundrede – se mere på
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