Egyptian President Mohammed Morsi has warned that continuing unrest is "threatening to paralyse the country".
In a speech marking his first year in office, Mr Morsi acknowledged making some "mistakes" and offered opponents a say in amending the new constitution.
But the president also threatened those he saw as conspiring against him and trying to "sabotage" democracy.
Troops have been deployed in cities across the country ahead of planned weekend protests demanding his removal.
Ahead of Mr Morsi's speech, deadly clashes broke out in the northern city of Mansoura.
Two people were killed and 170 injured in fighting between supporters and opponents of the government, a health ministry spokesman said.
Mr Morsi, who hails from the Muslim Brotherhood, became Egypt's first Islamist president on 30 June 2012, after winning an election considered free and fair. His first year in office has been marred by constant political unrest and a sinking economy.
In his two-hour televised address on Wednesday evening, Mr Morsi defended his performance, admitting errors and promising immediate and radical reforms to address them.
"I was right in some cases, and wrong in other cases," he said. "I have discovered after a year in charge that for the revolution to achieve its goals, it needs radical measures."
He apologised for the fuel shortages that have caused long lines at petrol stations and angered many Egyptians, and also for failing to involve the nation's youth enough.
But despite Mr Morsi's initial conciliatory tone, the speech swiftly moved into a condemnation of those he blamed for Egypt's problems, the BBC's Aleem Maqbool in Cairo reports.
"I took responsibility for a country mired in corruption and was faced with a war to make me fail," he said, naming several officials he believed wanted to "turn the clock back" to the Mubarak era, including politicians, judges and a journalists.
"Political polarisation and conflict has reached a stage that threatens our nascent democratic experience and threatens to put the whole nation in a state of paralysis and chaos," he warned. "The enemies of Egypt have not spared effort in trying to sabotage the democratic experience."
Mr Morsi called on opposition figures to "enter elections if you want to change the government" and criticised them for refusing to take part in a national dialogue.
The president said he would invite party leaders to meet on Thursday to choose a chairman for a committee that will prepare amendments to the constitution, approved in a referendum last year amid protests by secularists, liberals, women and minorities. He also said he was forming a committee of leading public figures to promote national reconciliation.
"I say to the opposition, the road to change is clear," he added. "Our hands are extended."
Anti-government supporters had gathered in the capital's Tahrir Square and outside the defence ministry ahead of Mr Morsi's speech.
The head of the army earlier warned it would not allow Egypt to slip into "uncontrollable conflict".
Soldiers have been stationed in areas of the capital, Cairo, where pro-Morsi demonstrators are expected to gather following Friday prayers.
Armoured trucks are lining the streets near Rabaa al-Adawiya Mosque in the city's east, which has become a gathering point for Islamist protesters.
Troops have also been deployed to protect the presidential palace - the scene of previous clashes - and other public buildings in Cairo.
Tensions in Cairo have been rising ahead of the demonstrations planned for the weekend, with counter-demonstrations by Islamists in support of Mr Morsi planned for the coming days.
There have also been acute shortages of fuel in the city, leading to huge traffic jams as well as long and sometimes bad-tempered queues at petrol stations, adding to the febrile atmosphere.
Some Cairenes have begun stockpiling food in anticipation of street clashes between the two opposing political camps, with staples including canned goods, grains and frozen vegetables much sought after.
Gen Abdul Fattah al-Sisi said the army was obliged to stop Egypt plunging into a "dark tunnel", in remarks which were seen as one of the strongest interventions since the army handed over power to President Morsi last year.
Anti-Morsi activists say they have gathered 13 million signatures on a petition calling for the Islamist leader to step down. They want early presidential elections to be called to replace him.
His supporters say any move to unseat him now would be undemocratic.
Many analysts say the instability and a continuing threat of violence have frightened away foreign investors and tourists.
There is increasing unemployment, particularly among the young, and the country's foreign currency reserves are falling.