Muslim Brotherhood candidate Mohammed Mursi claimed victory on Monday in Egypt's first free presidential vote, as the military handed itself sweeping powers in a move denounced by activists as a 'coup'.

A confirmed win by Mursi would mark the first time Islamists are elected to the presidency in the Arab World's most populous nation, but the military rulers' moves to consolidate power ahead of the final results have rendered any future president toothless.

The Islamists' rival Ahmed Shafiq, a former air force chief and ex-prime minister to ousted president Hosni Mubarak, disputed the Brotherhood's victory announcement, labelling it 'bizarre behaviour'.

State television too reported that initial counts showed Mursi in the lead.

There were scenes of jubilation at Mursi's headquarters, where the candidate himself thanked Egyptians for their votes in brief remarks after the Brotherhood said he had won 52 percent of the vote.

Mursi pledged to work to "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 Egypt's citizens, Muslims and Christians.

But a Shafiq campaign official said their figures showed that their candidate, who served as prime minister to deposed dictator Hosni Mubarak, leading in the count.

"We reject it completely," Mahmud Baraka, said of the Brotherhood's claim. "We are astonished by this bizarre behaviour which amounts to a hijacking of the election results."

Mursi's supporters screamed with excitement, some wiping tears from their eyes. Several hundred held a victory rally in Cairo's iconic Tahrir Square, the hub of protests that Mubarak in February 2011.

The jubilation was overshadowed however by a looming showdown between the Brotherhood and the ruling military, which issued a new constitutional document shortly after polls closed on Sunday granting it sweeping powers.

"The military hands power to the military," read the headline of the independent daily al-Masry al-Youm.

"A president with no powers," read the huge headline of the independent al-Shorouk.

Revolutionary youth movements denounced the declaration as a 'coup' while the Brotherhood's Freedom and Justice Party said it rejected any bid by the military to retake legislative power.

"The military council, with its unconstitutional coup, gave itself (unprecedented) powers. The military council has never and will never recognise popular legitimacy that contradicts it," the Coalition of Revolution Youth said in a statement.

The document issued by the Supreme Council of the Armed Forces grants the body legislative powers after a top court on Thursday ordered the dissolution of the Islamist-dominated parliament.

"The next phase is a very difficult phase," senior Mursi campaign official Khaled al-Qazaz said.

"It already started with the military trying to take all power, which requires all Egyptians to continue the momentum of the revolution to make sure the transition is complete."

The document gives SCAF veto power over the text of a new permanent constitution, and states that no new parliamentary vote will be held until after a permanent constitution is approved.

The Brotherhood called the interim charter "null and unconstitutional," setting itself on a collision course with the military.

The document was issued after last week's constitutional court ruling which found a third of the parliament's members had been elected illegally, effectively ordering the dissolution of the body.

"The Supreme Council of the Armed Forces shall exercise the powers referred to under the first clause of article 56 (on legislative power)... until the election of a new People's Assembly," the document reads.

Such an election cannot be held until a new permanent constitution is written and adopted by a referendum, it adds.

The writing of the new constitution will be carried out by a "constitutional commission representing all segments of the society" that will have three months to complete its work, the document says.

It also grants SCAF a veto right over any article of a draft constitution it considers "contrary to the supreme interests of the country."

Egypt's parliament has already appointed a constituent panel to replace an initial group that was dissolved over allegations it was Islamist-dominated.

But the declaration leaves it unclear whether that panel will be able to continue its work, and gives SCAF the right to form a new panel if the current body "is prevented from doing its work."

It also stipulates that SCAF "as currently constituted, has the power to decide on all matters related to the armed forces."

Parliamentary speaker Saad al-Katatni, an FJP member, said the constituent assembly appointed by the parliament would continue its work.

The presidential election had deeply polarised Egyptians, between those who objected to the Brotherhood's Islamist agenda and others who fear a return to the old regime under Shafiq.

The Brotherhood mobilised their formidable network of supporters to receive tallies from polling stations across the country and deliver early unofficial results, but final official figures are not expected until June 21.