Egypt's President Abdel Fattah el-Sisi has celebrated the 2013 overthrow of the country's first democratically-elected president by ordering a lavish military display in the capital and celebrations across the country.

Military jets roared over Cairo early on Thursday as Sisi addressed the nation in a pre-recorded address while his supporters were instructed to gather in the streets later in the evening after the breaking of the Ramadan fast.

"On this glorious day, I would like to assure you that we are working hard to realise the hopes of the Egyptian people for the better future they deserve," Sisi said in an early-morning televised speech.

The official holiday, which the government refers to as the "June 30 Revolution" was also marked with musical performances and free entry to museums.

"The June 30 Revolution reasserts the impossibility of imposing a status quo on the Egyptian people. Anyone who imagines that he can successfully do that is deluding himself," Sisi said, alluding to Mohamed Morsi's Muslim Brotherhood supporters.

PROFILE: Egypt's deposed president Mohamed Morsi

Morsi was toppled by the military in July 2013 following days of street protests by Egyptians demanding that he be removed.

Sisi was the military chief at the time who led the takeover and ran for president two years later, winning the vote in a landslide.

Sisi has since launched a persistent and extensive crackdown and has declared the Muslim Brotherhood a "terrorist organisation".

Thousands of Brotherhood members have been sentenced to death or life imprisonment, while others are standing trial or being held without formal charges.

Sisi spoke of "terrorism" in his speech and warned against anyone attempting to break Egyptians and their "hopes and dreams".

Security was stepped up across the country - where protests are effectively banned - but the day was punctured by violence in the Sinai Peninsula where a Christian priest was shot dead and two members of the country's security forces were killed in separate attacks.

READ MORE - The Egyptian revolution: What went wrong?

Also on Thursday, six members of Egypt's security forces were killed in clashes with smugglers on the country's western border.

The smugglers were trying to infiltrate Egypt from Libya, the military said in a statement, adding that several smugglers were killed.

On Wednesday, Sisi had appealed to security forces and agencies to stop anyone from "spoiling" the occasion.

In recent months, a growing number of Egyptians have begun losing patience with Sisi over corruption, poverty, and unemployment, the same issues that led to Mubarak's downfall, while Sisi has appeared increasingly defiant in his speeches.

In April, thousands of people marched Cairo in the biggest anti-government demonstrations since Sisi took office in 2014, shouting slogans such as "Down with the regime" and "Leave", both of which were used during the 2011 revolution that toppled former president Hosni Mubarak.