Crowds are marching through the Egyptian capital Cairo for rival rallies as emotions run high ahead of a referendum planned for Saturday.
The opposition have breached a barrier outside the presidential palace but there has been no violence.
Islamist President Mohammed Morsi, who called the vote to ratify a new constitution, has asked the army to maintain security.
Egypt has asked the IMF to delay a loan because of political turmoil.
Egypt requested the delay to the $4.8bn (£3.6bn) loan after President Morsi suspended a programme to increase taxes, Prime Minister Hisham Qandil told a news conference.
The International Monetary Fund says it "stands ready to continue supporting Egypt during the ongoing transition and to consult with the authorities on the resumption of discussions regarding the [loan].
The Egyptian economy has been hard hit by nearly two years of political upheaval since the protests which toppled ex-President Hosni Mubarak in February 2011.
Tanks and soldiers
Four separate opposition protest marches are due to converge on the presidential palace, which has been walled off with concrete blocks and ringed with tanks.
Hundreds of soldiers are guarding the palace perimeter.
Opposition protesters breached the temporary wall, but the BBC's George Alagiah, who is at the scene, says the Republican Guard allowed the demonstrators through. Several hundred are now in the palace compound.
The military is allowed to arrest civilians but has clearly decided not to use those powers, our correspondent says.
At least nine people were hurt early on Tuesday when shots were fired at opposition protesters in central Cairo.
The opposition wants the referendum scrapped, arguing that the constitution was drafted by an Islamist-dominated assembly, weakens human rights and fails to guarantee women's rights.
The president has tried to calm public anger by annulling a 22 November decree boosting his powers, but has given the army powers to arrest civilians over the next few days.
However, some rulings of his controversial decree - which stripped the judiciary of any right to challenge his decisions - will stand.
The general prosecutor, who was dismissed, will not be reinstated, and the retrial of former regime officials will go ahead.
Petrol bombs were thrown and shots fired at opposition demonstrators camping in Tahrir Square in the early hours of Tuesday.
Nine people received limb injuries from the unidentified attackers, while another protester suffered a head injury, Al-Misri al-Yawm newspaper reported.
After the attack, police cars were deployed around the square for the first time this month.
Pro-Morsi demonstrators from an umbrella group calling itself the Alliance of Islamist Forces - made of Muslim Brotherhood and Salafist groups - were also said to be gathering at two mosques in Nasser City, a suburb of Cairo.
The Muslim Brotherhood was reportedly hoping for two "million-man" marches to converge in support of the referendum and the president, under the slogan: "Yes to legitimacy."
Although their route was unclear, spokesman Mahmoud Ghozlan told state-owned al-Ahram newspaper that there was no plan to head for the presidential palace.
Hundreds of Islamist demonstrators were also staging a sit-in outside a Cairo media complex that hosts the studios of several private TV channels, which pro-Morsi protesters accuse of bias.
Seven people died and hundreds more were wounded in clashes between rival protesters outside the palace last Wednesday night.
There are fears there could be more violence if rival groups of protesters come face to face, the BBC's Jon Leyne in Cairo reports.
Because several anti-Morsi marches have been organised across Cairo, they could potentially cross paths with the main pro-Morsi demonstrations.
Protests have also been planned in the cities of Alexandria and Assiut.
The army presence on the capital's streets has also raised fears Egypt is moving back towards military rule, our correspondent says.
President Morsi granted the army powers of arrest on Sunday until the results of Saturday's referendum were announced, calling on the military to co-ordinate with the police in maintaining security.
The police, seen as a weakened force since the fall of ex-President Hosni Mubarak, failed to intervene when anti-Muslim Brotherhood protesters ransacked the Islamist movement's Cairo headquarters last week.
By pressing ahead with a referendum on the constitution, the president says he is trying to safeguard the revolution that overthrew the former president last year, but critics calling for large turnouts at Tuesday's protest accuse him of acting like a dictator.
The opposition National Salvation Front has said it will not recognise the draft constitution, as it was drafted by an assembly dominated by Mr Morsi's Islamist allies.
NSF chief co-ordinator Mohammed ElBaradei said the "sham" draft constitution defied Egyptians' "basic rights of freedom".
"It doesn't establish proper democratic systems, so at this stage at least we have decided that we are going to continue to fight tooth and nail against the referendum," the Nobel peace prize winner told the BBC.
Mr ElBaradei would not go so far as to call for a boycott of Saturday's vote, but said he hoped the turnout at Tuesday's protests would persuade Mr Morsi to postpone the referendum until consensus was reached through dialogue on a "proper, democratic" constitution.
Meanwhile, Mohamed Soudan, foreign relations secretary of the Muslim Brotherhood's Freedom and Justice Party, said Mr Morsi was constitutionally bound to go ahead with Saturday's vote because the date had been announced by the constituent assembly.