Ex-army chief Abdul Fattah al-Sisi has vowed to to tackle "terrorism" and bring security, after being sworn in as Egypt's new president.
He said his election after a landslide win in May was "a historic moment", and pledged no reconciliation with those who had "committed violence".
The retired field marshal overthrew President Mohammed Morsi last July.
He has since been pursuing a crackdown on Mr Morsi's Muslim Brotherhood, which urged a boycott of the elections.
Liberal and secular activists, including the 6 April youth movement which was prominent in the 2011 revolution that ousted long-serving President Hosni Mubarak, also shunned the 26-28 May poll in protest at the curtailing of civil rights.
Mr Sisi, 59, made no mention directly of the Muslim Brotherhood in a speech at a Cairo presidential palace late on Sunday.
But he said there would be no reconciliation with anyone who had "blood on their hands".
He said: "Defeating terrorism and achieving security is the top priority in our coming phase.
"There will be no acquiescence or laxity shown to those who resorted to violence."
Mr Sisi was earlier sworn in for a four-year term at a ceremony shown live on television.
He said: "Throughout its extended history over thousands of years, our country has never witnessed a democratic peaceful handover of power."
Mr Sisi's victory came almost a year after he ousted Egypt's first freely elected president, Mohamed Morsi, following mass protests against his rule.
At the swearing-in, the Supreme Constitutional Court deputy head, Maher Sami, said the ousting was not a coup, and that Mr Sisi had responded to the will of the people.
Who is Egypt's new president?
- Born in Cairo in 1954
- Had long military career, latterly specialising mainly in military intelligence
- Appointed army chief under Mohammed Morsi
- Key figure in interim government after ousting Morsi in July 2013
In the May elections, Mr Sisi secured 96.9% of the vote and his sole challenger, left-winger Hamdeen Sabahi, received only 3.1%. Turnout was less than 50%.
Mr Sisi inherits a nation that is divided and weary, the BBC's Orla Guerin in the Egyptian capital reports.
Experts warn that if he cannot deliver in the next year or two he could also face a mass revolt.
One student, Israa Youssef, told Reuters: "Sisi has to do something in his first 100 days, people will watch closely and there might be another revolution. That's what people are like in this country."
Mr Sisi faces an array of challenges, including fixing the economy, preventing further political crises and easing poverty.
More than a quarter of Egyptians live below the poverty line. Mr Sisi has pledged to build 26 new tourist resorts, eight new airports and 22 industrial estates.
He has promised to restore security in a country where attacks by Islamist militants have left hundreds of security personnel dead over the past 11 months.
The militants have stepped up attacks in response to the crackdown on the Muslim Brotherhood and its allies, in which more than 1,400 people have been killed and 16,000 detained.
Mr Morsi and other senior leaders of the Brotherhood, which has been designated a terrorist organisation, are standing trial on a series of charges. They strongly deny any wrongdoing.
Critics fear Mr Sisi will continue to show little tolerance for dissent.