The African Union (AU) says the army acted unconstitutionally when it took over after President Blaise Compaore was forced to resign on Friday.
The AU on Monday gave the army a two-week deadline. Interim leader Lt Col Isaac Zida later promised to comply.
Mr Compaore quit after mass protests at his bid to extend his 27-year rule.
Col Zida met Senegalese President Macky Sall, Goodluck Jonathan of Nigeria and Ghana’s John Mahama at the airport in the capital Ouagadougou.
A statement from President Jonathan’s office said the three-man delegation representing West African regional body Ecowas aimed to “facilitate the rapid resolution of the current political crisis in Burkina Faso”.
They will hold a series of meetings to press for the quick handover, following a threat by the AU to impose sanctions if the military did not act within two weeks.
The BBC’s Emmanuel Igunza in the Ethiopian capital Addis Ababa says the sanctions could include suspension of Burkina Faso’s AU membership and a travel ban on military officials.
After meetings with opposition leaders and activists on Tuesday, Col Zida was quoted as saying that he would comply with the demand.
“If everyone agrees, there is no reason that the transition shouldn’t be done within two weeks,” he said, according to union leader Joseph Tiendrebeogo, the AFP news agency reports.
Opposition leaders have not entirely ruled out a role for the military in the transition.
Col Zida was previously second in command of the presidential guard.