Twelve people were killed in one area of the capital over the weekend, several witnesses told Agence France-Presse, while a source from the Red Cross said four had died in another part of Bangui, and three more elsewhere in the city.
Police added that the clashes erupted as Seleka members were searching for weapons among residents.
"We don't have all the details on the victims but after what we saw and the information we get from other medical sources, there are close to 20 dead," said a source at a Bangui hospital morgue.
Police said that according to first reports at their disposal and those provided by the Red Cross, there were "nearly 20 dead and dozens of wounded", adding that the toll could rise.
Witnesses contacted by AFP said there were 12 dead in the capital's seventh district where mayor Joseph Tagbalet was among the wounded and taken to hospital.
The shootings led residents to flee across the Oubangui River to neighbouring Congo.
The Seleka coalition, led by strongman Michel Djotodia, took power in a rapid assault on the capital on March 24, the latest coup in the notoriously unstable country.
A taxi driver said a Seleka member had opened fire on a young man holding a rickshaw with a body to bury, and who died on the spot. "That infuriated the mourners and the residents of the neighbourhood. Screaming and shouting followed," he added.
The Red Cross said that four people died in the Boy-Rabe district and three more in Gobongo.
Boy-Rabe was the scene of tensions last week when shots were fired but no one was killed.
Djotodia, who was on Saturday elected interim president by the national transitional council, singled out "a group of individuals" who continue to support ousted president François Bozizé for the latest violence.
They "want to push Central Africans into civil war so they will kill each other", he said on national radio.
"But the Central Africans do not want this to happen and they do not want to be at war with each other."
"What happened these past 48 hours at Boy-Rabe [happened] because our men went to this area … but those longing for the Bozizé era … killed our men and dumped the bodies at Ngaragba to blame [the killings] on Ngaragba residents," he said.
Seleka has so far failed to restore order in the capital after seizing power and Bozizé's flight as the rebels advanced. He is now expected to seek asylum in Benin.
A statement signed by "François Bozizé's department of communication" and received by AFP meanwhile said he "firmly condemns the coup … which only aims to allow foreign commissioners to grab our country's natural resources".
"A large part of the Central African territory is left to organised pillaging of its mining resources including by multinational companies, as the international community looks on complacently," it said.
The statement added that "hundreds are dying, private property and public buildings are being destroyed, Christian churches vandalised, clerics abused but nobody cares".
Before the weekend violence, the Central African Red Cross had put the number of dead and wounded in the Seleka takeover at 119 and 456 respectively. – AFP