Three people were killed on Saturday in a Port-au-Prince neighbourhood. The dead included Sergeant Ravix Remissainthe, the self-declared leader of former soldiers, a source close to the Haitian police said.
At least 18 other people were arrested the same day. No deaths were reported among the police.
Seven others were killed on Sunday near the capital's airport in a shootout with police, the source said.
The victims included former soldier Jean Rene Anthony, who was wanted by the authorities for his alleged involvement in the February killing of four police officers.
The Haitian government has
promised to solve the crime issue
Anthony was among a group of former soldiers occupying public buildings and some police stations to demand that the interim government restore the Haitian army.
Ousted president Jean Bertrand Aristide, who fled the country last year amid an armed uprising, disbanded the army in 1995.
Aristide had previously been toppled in a military coup in 1991.
A UN stabilisation force was sent to Haiti last year after Aristide's departure.
Tackling crime, violence
Interim Prime Minister Gerard Latortue, who had lunch with Florida governor Jeb Bush and Haitian and US business leaders in Miami, said of the wave of violence in Haiti: "We are really going fast in solving the problem."
Meanwhile, a working group created by Bush, whose state is home to 230,000 Haitians, issued recommendations on how Florida can help Haiti's security and development.
The group also asked that the Florida state urge the US federal government to lift an embargo on non-military weapons against Haiti.
Bush, brother of US President George Bush, said the recommendations were "doable".