In an almost 40-minute televised address, Sisi also said the jihadist targets that his country's air force struck in neighbouring Libya last week had been carefully chosen to avoid civilian casualties.
Sisi has come under increasing criticism for a deadly crackdown on Islamists that has also ensnared secular dissidents, but he remains popular among Egyptians who say the country needs a firm hand.
Unlike in recent speeches, Sisi appeared relaxed in the taped address, and gently addressed some of the criticisms of his presidency.
He said journalists had complained that there were innocent people in jail, so he told them to draw up a list.
"I told them I don't deny there might be innocent youths" in prison, Sisi said.
"Over the next few days the first group of our youths in detention will be released," he added.
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Rights groups say that more than 20,000 people, mostly Islamists, have been jailed in the crackdown since the then army chief toppled Islamist president Mohamed Morsi in July 2013.
The country has also seen a string of militant attacks that have killed scores of policemen and soldiers, and last week there were calls for Sisi to act after jihadists in Libya beheaded 21 mostly Christian Egyptian hostages.
"I couldn't offer my condolences until your armed forces had taken revenge," he said of the early morning air strikes on February 16, hours after the Islamic State group released gruesome footage of the beheadings.
"Thirteen targets were struck -- they were all carefully checked," he said. "No one should think we attacked civilians."
He made no mention of further air strikes and did not repeat a demand for global action against the jihadists in Libya, a call which had met Western opposition.
Sisi also suggested that a leaked recording in which he and aides purportedly derided powerful Arab Gulf donors had been fabricated, after an opposition-linked television station aired the tape.
After the release of the recording earlier this month, Sisi called several Gulf Arab leaders who had donated billions of dollars to Egypt to express his support for them.