Leading opposition figure Moise Katumbi warned against any move that sought to gain time for Kabila or weaken the accord
The demand touches on a key phase for implementing a historic deal, forged on New Year's Eve, for hauling Democratic Republic of Congo out of a dangerous impasse.
Mediated by the Roman Catholic Church, the accord sketches a timetable under which Kabila will stay in office before new elections are held.
The coalition said the mediation mandate had to be renewed and approved by Kabila himself in exchange for the government to discuss transition arrangements.
"The bishops must first present the report ... to the president, who must reconfirm, using his discretionary powers, the bishops' mandate," said coalition secretary general Aubin Minaku.
"It's time to respect the prerogatives of the president of the Republic, and the constitution and institutions," he added.
Leading opposition figure Moise Katumbi warned against any move that sought to gain time for Kabila or weaken the accord.
"Any foot-dragging, tricks or blocking manoeuvres will not be tolerated," Katumbi, who lives abroad, said in a statement.
The bishops have asked both sides to submit written proposals Wednesday on arrangements for issues including the naming a new prime minister and the size of the government.
Under the country's constitution, Kabila should have left office on December 20 at the end of his second and final mandate, but he has shown no sign of wanting to step down.
Scores of people died in clashes in the runup to the deadline, prompting the church, which wields considerable clout, to ramp up efforts for a political solution.
Under the deal, 45-year-old Kabila will stay in power until elections are held "at the end of 2017."
During the 12-month period, a transitional body will be set up, headed by the 84-year-old opposition leader Etienne Tshisekedi, and a prime minister will be named from opposition ranks.
Christophe Lutundula, who signed the agreement for the opposition, said the next talks would be about "specific arrangements" for the transitional body, named the National Council for Overseeing the Electoral Agreement and Process (CNSAP).
Issues include methods for appointing CNSAP's 28 members and "the composition of the (transitional) government," Lutundula told AFP.
Kabila took office after his father Laurent was assassinated in 2001 at the height of the Second Congo War.
He was confirmed as leader in 2006 during the first free elections since independence, and re-elected for a second term in 2011 in a vote marred by accusations of fraud.
Endowed with natural resources but chronically poor, sapped by corruption and politically unstable, the Democratic Republic of Congo has never witnessed a peaceful transfer of power since it gained independence from Belgium in 1960.
The former colonial ruler has joined others in the international community in piling pressure on the political factions to stick to the agreement.