Previous reports indicated that 23 suspects were detained. The list of the detainees includes 18 Colombian and five Haitian citizens.
"Three more people have been detained," Director General Leon Charles told reporters late on Tuesday, as broadcast on the police's Facebook account.
There are police officers among those detained, Charles added.
Haiti plunged into a crisis after Jovenel Moise and his wife, Martine Moise, were shot at their private residence last week. The First Lady suffered a severe abdominal injury and was airlifted to a hospital in Miami for treatment. On Monday, Joseph confirmed that she was feeling well and was recovering.
The police said that they had identified 28 suspects, including 26 Colombian nationals and two US nationals.