The Head of State was speaking to journalists before departure for Northern Province on a three day working visit.
President Lungu said Hichilema’s treason case will be dealt with according to the law.
He said the people that arrested Hichilema will be left to do their jobs without his interference.
Hichilema has been charged with treason and six other offences following the incident in Mongu on Saturday where he refused to give way to the Presidential motorcade.
On Monday night police raided Hichilema’s house and arrested him around 11:00 hours on Tuesday and have been holding him at Lilayi Police Training College.
On Wednesday Inspector General of Police Kakoma Kanganja confirmed that Hichilema had been charged with treason and also failure to obey lawful orders among other charges.
“Let’s allow each other space to do that which we have been assigned in our calling. As the President, I know my job and these people also as law enforcement authority they know their job, even lawyers know their job,” said President Lungu.
“People calling upon me to intervene in the operations of the police, we don’t do that in a civilised state. The rule of law demands that the law is above all of us so those who are calling upon me to intervene or interfere in areas which are not under my control, I will not do so. Let us respect each other’s roles.”
He added: “There’s the Legislature, the Executive, the Judiciary, President, Police Inspector General, all of us have got roles. Why do they want me to have all the power which I don’t have? I don’t have power.”
Hichilema has since applied for a writ habeas corpus seeking that the law enforcement officers bring her before the courts of law.
His writ of habeas corpus hearing has been adjourned to next Tuesday leaving him to spend the Easter weekend behind bars.
The maximum punishment for treason is the death sentence.
Meanwhile, President Lungu stepped out of the politically charged Lusaka to get down working in Northern Province.
The Head of State is in Northern Province on a three day working visit as he touches base with development projects in the country.
President will pay homage to paramount Chief Chitimukulu and hold a number of rallies in Kasama, Mungwi and Mporokoso.