Egyptians have gone to the polls in a two-day run-off election to choose their first freely-elected president.

The election sees Mohammed Mursi, the head of the Muslim Brotherhood, face Ahmed Shafiq, Hosni Mubarak's last prime minister.

The ruling Supreme Council of the Armed Forces has promised to hand over power to the winner by the first of July at the latest.

50 million Egyptians are eligible to cast ballots in the election.

Long queues had already formed outside some voting stations before the polls opened at 8am (7am Irish time), with police and army deployed outside, according to AFP reporters.

The voting comes against the backdrop of two controversial court rulings on Thursday, allowing Mr Shafiq's candidacy to proceed despite his role in the old regime, and invalidating Egypt's elected parliament.

The choice of candidates has garnered support for the boycott movement with celebrities and high-profile activists calling on Egyptians to abstain or void their ballot.

The winner will be the first freely chosen president in Egypt's history and will succeed Mr Mubarak, who was forced from office by a popular revolt last year and turned power over to the military.

Activists said the court rulings were the final phase of a military coup that takes the democratic transition back to square one.

"Back to where you were," read a huge red headline in the independent daily Al-Shorouk after the Supreme Constitutional Court said certain articles in the law governing parliamentary elections were invalid, annulling the Islamist-led house.

It also ruled unconstitutional the political isolation law, which sought to bar senior members of Mr Mubarak's regime and top members of his now-dissolved party from running for public office for 10 years.

Activists opposed to Mr Shafiq had hoped the court would uphold the law and bar him from the presidential race.

Mr Shafiq had initially been barred from standing, but the electoral commission accepted his appeal last month, permitting his candidacy and referring the case to the court.

Following the ruling, activists accused the ruling Supreme Council of the Armed Forces (SCAF) of staging a "counter-revolution" after a series of measures that consolidated its power ahead of the polls.

On Wednesday, the Justice Ministry decided to grant army personnel the right to arrest civilians after that power was lifted when a decades-old state of emergency expired on 31 May.

"[T]he head of the counter-revolution, is adamant to bring back the old regime, and the presidential elections are merely a show," six parties and movements said in a joint statement.

US Secretary of State Hillary Clinton called for a full transfer of power to elected civilians.

"There can be no going back on the democratic transition called for by the Egyptian people," she told reporters in Washington.

But the State Department said separately it was "troubled" by the court ruling ordering parliament annulled and was studying its implications.

"We are continuing to monitor the situation in Egypt," spokeswoman Victoria Nuland said.

"If in fact the conclusion is that there need to be new parliamentary elections our hope is that they can happen swiftly and that they reflect the will of the Egyptian people."

Parliament speaker Saad al-Katatni, a member of the Muslim Brotherhood, whose Freedom and Justice Party won 47% of seats in the house, said there were "question marks over the timing of the ruling."

A military source said the court ruling technically meant that the military would assume legislative powers.