Several thousand Egyptians took to Tahrir Square on Tuesday to protest against the ruling military's bid to grab new powers, as both presidential candidates claimed victory in a historic vote.

In the hub of the uprising that ousted president Hosni Mubarak, protesters chanted against his military successors, with many more expected to join them as the temperature drops.

The demonstration comes against a backdrop of uncertainty over the winner of the presidential vote, with the Muslim Brotherhood candidate Mohammed Mursi and his rival former prime minister Ahmed Shafiq both claiming victory.

The Brotherhood said it would participate in Tuesday's protest, called by several groups that participated in Egypt's 2011 uprising, against measures by the ruling military council to claim sweeping powers.

Just as counting began in the pivotal presidential polls late on Sunday, the Supreme Council of the Armed Forces (SCAF) issued a constitutional declaration claiming legislative power after a court ordered parliament's dissolution.

The declaration also gives the council veto power over the wording of a new permanent constitution and appeared to interfere with the ability of the incoming president to exercise his powers.

With official results in the presidential poll, the first since the uprising that ousted Hosni Mubarak, not expected before Thursday, both camps claimed victory for their candidates.

At a news conference on Tuesday, Mursi's campaign released what they said were the certified figures, which they said showed their candidate taking 52 percent of the vote.

Hours later, Shafiq's campaign insisted he had won the election with 51.5 percent of the vote.

"We are certain that the next president of Egypt is General Shafiq," his campaign spokesman Ahmed Sarhan told reporters.

He had earlier insisted it was ‘an act of piracy to claim victory using totally false figures’ and said Shafiq was ahead.

Egyptian state media also reported that counts showed Mursi ahead.

A confirmed win for Mursi would mark the first time the Islamists have taken the presidency of the Arab world's most populous nation.

After campaign officials announced his projected victory Sunday, there were scenes of jubilation at Mursi's Cairo headquarters from where the candidate pledged to work ‘hand-in-hand with all Egyptians for a better future, freedom, democracy, development and peace’.

"We are not seeking vengeance or to settle accounts," he said, adding that he would build a ‘modern, democratic state’ for all Egyptians, Muslims and Christians alike.

No matter who emerges as the winner, the country faces the prospect of a showdown between the Brotherhood and the ruling military.

"The Brotherhood and the military council prepare for the battle of the parliament," the headline of the liberal Wafd newspaper read Tuesday.

The Brotherhood insists the parliament still has the power to legislate and said Monday it would take part in ‘all popular activities against the constitutional coup and the dissolution of parliament, beginning on Tuesday’.

On Tuesday, a few hundred demonstrators gathered outside a heavily guarded parliament to oppose the body's dissolution, with the numbers expected to swell later.

The ruling military body has introduced de facto martial law, given itself control of the legislature and state budget and also granted itself veto power on a new constitution.

Revolutionary youth movements, which had been split over whether to boycott the election or to vote Shafiq out, denounced the move as a "coup" and the Brotherhood has vowed to challenge the constitutional declaration.

The military on Monday sought to quiet fears over the declaration, insisting it will transfer power to the new president on schedule by the end of this month, and pledging the new leader would enjoy full powers.

"The president of the republic will be vested with all the powers of the president of the republic," a ruling SCAF General Mohammed al-Assar told reporters.

France on Tuesday called for a speedy return to democracy in Egypt.

"A quick and orderly handover of all powers to the civil authorities elected democratically is the best way to respond to the aspirations of the Egyptian people", foreign ministry spokesman Bernard Valero said.