EU foreign policy chief Catherine Ashton has voiced approval of Egypt's referendum on a new constitution, but said she expected it to usher in civilian leadership.
She welcomed the vote taking place "in a largely orderly manner," while noting in her statement that turnout was officially recorded at under 40%.
Egyptian election officials said yesterday the new constitution, which does away with changes introduced under ousted Islamist president Mohammed Mursi, was approved by 98% of ballots cast in the Tuesday-Wednesday vote.
Mr Mursi's Muslim Brotherhood and other Islamists boycotted the referendum.
Ms Ashton said the EU could not verify alleged irregularities but said "these do not appear to have fundamentally affected the outcome".
She added: "I do however strongly regret the violent clashes related to the referendum leading to deaths and injuries on all sides in protests."
While Egyptian army chief Abdel Fattah al-Sisi, the general who led Mursi's overthrow, was seen as possibly aiming to launch a presidential bid, Ms Ashton said the new constitution should be applied "in a way that gives full effect to civilian pre-eminence".
Mohammed Mursi to stand trial
Mr Mursi and 24 others, including activists who opposed him and his predecessor, will stand trial on charges of insulting the judiciary.
The defendants allegedly made comments in the media and online that showed "disrespect and hatred for the courts and the judiciary," state news agency MENA said.
It was unclear whether all 25 accused would be tried together.
The latest charges mark the fourth set of legal proceedings against Mr Mursi since he was deposed by the army in July.
MENA said Mr Mursi stands accused of giving a speech days before his ouster, when he allegedly accused a judge of overseeing electoral fraud in a 2005 vote.
Mr Mursi, Egypt's first freely elected civilian president, is already on trial for inciting the killings of opposition protesters in December 2012 outside the presidential palace.
His second trial over a prison break during the 2011 uprising is to start on 28 January, while no date has yet been set for his third trial on charges related to espionage.
Other defendants in the trial for insulting the judiciary include several Islamists as well as Alaa Abdel Fattah, one of the activists who led the revolt against Hosni Mubarak in 2011.
He is already in detention for participating in an illegal protest in November.
Abdel Fattah has been charged over comments on Twitter several months ago.
The comments were about legal proceedings concerning 2011 raids on the offices of foreign civil society groups, said his father and lawyer Ahmed Seif al-Islam.
Amr Hamzawy, a well known political science professor, and human rights lawyer Amir Salem will also stand trial.
The pair had backed the ouster of Mr Mursi in July along with Abdel Fattah.
Mr Salem, who represented families of slain protesters in Mubarak's murder trial, said he has been charged over comments he made related to this case.
"I am very surprised to find myself among (leaders) of the Brotherhood and the (Islamist) Gamaa Islamiya after I opposed them," he said, adding he had consistently fought "for the independence of the judiciary".
The other Brotherhood leaders to stand trial include former parliament speaker Saad al-Katatni, and Mohammed al-Beltagi, the secretary-general of the Brotherhood's political Freedom and Justice Party.
Egyptian judicial sources, meanwhile, said the Brotherhood's supreme guide Mohammed Badie will stand trial.
He will be tried with more than 50 other supporters of Mr Mursi on 1 February.
They are charged with inciting violence that left two people dead in the Nile Delta city of Qaliub, shortly after the ouster of Mr Mursi.
It will be the third trial of Mr Badie and include other Brotherhood figures such as Beltagi and Essam El-Erian.
Mr Badie and 14 other Brotherhood members are already on trial for inciting violence in the Cairo neighbourhood of Bahr al-Aazam that led to deadly clashes in July.
Mr Badie and his two deputies, Mr Khairat al-Shater and Rashad Bayoumi, are also being tried on separate charges related to the deaths of protesters who stormed the Brotherhood's Cairo headquarters on 30 June.