The Economic Community of West African States (ECOWAS) slapped sanctions on Mali after the putsch, including closing borders and a ban on trade and financial flows, and has called for elections within 12 months.
The 15-nation bloc also gave the new military rulers until Tuesday to name a civilian president and prime minister to head a transition government.
"My reason for this meeting is simple. We need to bring finality to our deliberations on Mali," Ghanaian President Nana Akufo-Addo said in an opening statement at a lodge at Peduase, eastern Ghana.
"That country can no longer afford any delay in putting a responsible government in place."
Akufo-Addo, the current ECOWAS rotating chairman, reiterated that Tuesday was "supposed to be the day the military junta is supposed to put in place a government".
"A closure should be brought to the matter now," he said.
Junta leader Colonel Assimi Goita, who was appointed interim head of state, was attending the talks on his first trip abroad since seizure of power.
He was set to deliver a speech behind closed doors to the assembled leaders from across the region outlining the putschist's plans.
The military junta over the weekend backed an arrangement for an 18-month transition government, but this was rejected by Mali's popular opposition movement.
Mali's neighbours, who are anxious to avoid the fragile Sahel state spiralling into chaos, have not yet reacted to the transition roadmap.
Last month's coup -- Mali's fourth since gaining independence from France in 1960 -- came after months of protests stoked in part by Keita's failure to quell a jihadist insurgency that has plagued the country since 2012.
The violence has since spread to neighbouring Burkina Faso and Niger.