Odero, a wealthy televangelist who boasts a huge following, is being investigated on a raft of charges including murder, aiding suicide, abduction, radicalization, crimes against humanity, child cruelty, fraud and money laundering.
Kenyan police had arrested Odero last Thursday over the "mass killing of his followers" and closed his New Life Prayer Centre and Church that lies south of the coastal town of Malindi.
Prosecutors accuse Odero of links to cult leader Paul Nthenge Mackenzie, who is in custody facing terrorism charges over the deaths of more than 100 people, many of them children, in what has been dubbed the "Shakahola forest massacre."
Police are seeking to hold Odero, who is popularly known as Pastor Ezekiel, for another 30 days to enable their investigations to be completed.
Prosecutors have said in court documents that they have credible information linking the corpses exhumed at Shakahola to the deaths of several of Odero's "innocent and vulnerable followers."
Police are also investigating information that the bodies were kept in a privately-run morgue before being transported and buried in the forest, according to the documents.
About 50 Odero supporters gathered outside the courtroom in the Indian Ocean port city of Mombasa, some dressed in all white, some in red, and praying with bibles in hand.
Mackenzie, the head of the Good News International Church, is alleged to have incited his followers to starve to death in order to "meet Jesus" in a case that has deeply shocked Kenyans.
A total of 109 people have so far been confirmed dead in the Shakahola forest case, the majority of them children.
Autopsies carried out so far on about 40 of the bodies unearthed in the forest inland from Malindi found that while starvation appeared to be the main cause of death, some of the victims were strangled, beaten or suffocated.
In a court filing earlier this week, Odero said he wanted to "strongly disassociate" himself from Mackenzie and disagreed with his teachings.
Odero claims that "holy" scraps of cloth and water sold at his mega-rallies for 100 Kenyan shillings (75 U.S. cents) can heal any disease, including HIV - provided people have a strong faith.
Mackenzie himself is due back in court in Mombasa on Friday with another 17 co-accused, where prosecutors are expected to ask for him to be detained for 90 days.
The deeply religious Christian-majority country has been stunned by the case and President William Ruto has pledged to take action against unscrupulous churches and cults that have dabbled in criminality.