The decision was made as investigators continue to gather evidence linked to the incident.
During the court session, the second respondent, Anne Mueni Muthama, was present and appeared before the judge.
However, the first respondent, Kennedy Mutie Mbithi, did not attend the proceedings after being hospitalised due to high blood pressure.
The court was informed of his condition and allowed the matter to proceed in his absence.
The Office of the Director of Public Prosecutions (DPP) told the court that investigations into the murder are still ongoing and require at least 10 more days to be completed.
Prosecutors said the additional time is necessary to allow police to finalise key forensic and medical procedures.
One of the critical steps yet to be carried out is a postmortem examination on the body of the deceased.
According to investigators, the postmortem results will help establish the exact cause of death and provide important medical evidence for the case.
The court was also informed that firearms and ammunition recovered from the crime scene have been forwarded to the cybercrime unit in Nairobi for detailed analysis.
The examination is expected to determine whether the weapons were used in the killing and if they are linked to any other criminal activities.
Prosecutors argued that releasing the suspects at this stage could interfere with ongoing investigations.
They maintained that holding the suspects in custody would ensure the integrity of the case and protect witnesses who are yet to record statements.
The defence did not strongly oppose the request for more time but asked the court to consider the health condition of the absent suspect.
The judge directed that Mbithi continue receiving medical care while in custody and that his health status be closely monitored.