In an interview broadcast on Egyptian satellite networks last night, the former army chief alleged that the Brotherhood had links with violent militant groups and that two plots to assassinate him had been uncovered.
Sisi, 59, who ousted Morsi last July after mass protests against Egypt's first democratically elected president's rule, vowed to finish off the Muslim Brotherhood if won the May 26- 27 presidential election, arguing that's what his country's people want.
"I want to tell you that it is not me that finished (the Brotherhood). You, the Egyptians, are the ones who finished it," Sisi said in a joint interview with Egypt's privately owned CBC and ONTV television channels.
Asked whether the Brotherhood would cease to exist if he should win the presidency, the answered: "Yes. That's right."
He said there had been two attempts to assassinate him, but added: "I believe in fate, I am not afraid."
He did not provide details of who was behind the alleged plots or how advanced they were.
Sisi also denied being the candidate of the army, saying "the army would not have a role in ruling Egypt". He resigned from his military post in March to run for the presidency.
Since Morsi's overthrow, more than 1,000 people have been killed and thousands of members of Muslim Brotherhood detained by authorities, who have designated the Islamist movement a terrorist group.
A court sentenced the Supreme Guide of the Brotherhood, Mohamed Badie, and hundreds of supporters to death last week over an attack on a police station in Minya in 2013 in which a policeman was killed.
Analysts say Sisi is expected to easily win the election. The only other candidate is leftist politician Hamdeen Sabahi, who came third in the 2012 election won by Morsi.
Sisi also said he had no choice but to run for President.
"Due to the challenges facing Egypt and the targeting of Egypt from inside and outside of the country ... any responsible patriot has a duty toward his country and its future, and has the opportunity to come forward to protect this country, and this people, and their future," he said.
Sisi is popular among Egyptians who supported the army's decision to remove Morsi from power. His supporters see him as the kind of strongman needed to end the turmoil dogging Egypt since a popular uprising ended Hosni Mubarak's three decades of one-man rule in 2011, CNN reported.
But Sisi is reviled by the Islamist opposition, which sees him as the mastermind of a coup against an elected leader and the author of a fierce crackdown on dissent, it said.