Hichilema was taken into police custody this week for allegedly refusing to give way to Lungu's motorcade as it passed through Mongo, 500 km (300 miles) west of the capital Lusaka, last Saturday.
His party, the United Party for National Development (UPND), has denied any wrongdoing and said a hearing was due next Tuesday to determine if Hichilema's detention is legal.
"Some people are saying President Lungu has the power to intervene in the criminal justice here in Zambia. I am a lawyer myself and understand my job. Yes, I have the power to pardon convicts and not suspects," Lungu said at a public rally broadcast on state television late on Friday.
"How many of my own cadres are before the courts of law today? How many have been convicted? Have you ever heard that President Lungu picked up a phone to call any police officer to drop an investigation or prosecution? – so what is so special about the current one?"
Tensions between the government and opposition have escalated since August, when Lungu's Patriotic Front (PF) party narrowly beat the UPND in a vote the opposition says was rigged.
Under Zambia's penal code, treason carries a death sentence and is non-bailable.
The European Union has called for calm.