Hussain Abd al-Ghani, Aljazeera's Cairo bureau chief, said the turnout on Wednesday was limited although turnout in rural areas proved to be higher than in urban areas.
He said turnout in the rural south reached about 30-35%.
Aljazeera said members of Kifaya (Enough) movement were beaten up by club-wielding police officers after the group protested near a polling station.
Polling stations around Egypt have officially closed, he added.
But one officer at a polling station in Cairo's Khedive secondary school said: "I can't say that more than three to five percent turned up today."
In other schools, employees clumsily attempted to hide electoral registers on which most names had not been ticked off.
"Maybe we got 30% or more," an employee at Ahmed Lufti primary school said. But thick stacks of unused ballot papers were piled up on his desk.
Policemen deployed to protect polling stations countrywide quickly intervened to prevent electoral officers from revealing more and asked journalists to leave.
Policemen in plainclothes had a
busy day tackling protesters
Reports from the provinces suggested turnout was higher there but the level of participation was clearly well short of the endorsement the authorities had been seeking for a controversial reform slammed as a sham by the opposition.
In an eve-of-polling-day address, Mubarak had told Egypt's 32.5 million registered voters: "The last word is yours. I have complete trust in your will to participate to open new horizons for our political life."
But even among the government loyalists who did turn up to vote, few seemed to understand what they were being asked to vote for.
Several voters quizzed by journalists said they thought they were being asked to re-elect Mubarak for a fifth six-year term, not vote on a constitutional amendment supposedly paving the way for a challenger to stand against him in September.
Kifaya movement activists were
beaten up by police in Cairo
"I said yes to the president, of course, because what we know is better than what we don't know," said one woman who turned up at a polling station in Cairo's Qawmiya school.
Her comments came despite an array of banners across the school's facade urging support for the government's proposed amendment.
Yes to Mubarak!
"Yes to Mubarak! Yes to more reforms! Yes to constitutional change!" they said.
It was the same story at the Khedive school.
"I'm here to vote for Mubarak," Hamada, 24, said.
Mubarak supporters also made
their voices heard on Wednesday
Her mother nodded her approval. "Mubarak must stay as president. We are here to re-elect him," she said.
Polling officers acknowledged that such misunderstandings were widespread among voters used for decades to single-candidate elections for the presidency.
"Many people thought they had to vote for the presidency and we had to tell them it was for the amendment," one officer said.
Mubarak stood unopposed for his four previous terms in office after being approved as sole candidate by a legislature dominated by his ruling National Democratic Party.
Analysts had said all along that voter turnout would be the key test in the referendum, rather than the number of votes cast for or against the amendment.
Opposition parties from the Marxist left to the Islamist right had called for a boycott in protest at the major hurdles still put in the way of the registration of challengers to Mubarak.
Turnout in rural areas was said to
be higher than that in the cities
The main issue in the referendum will be "the turnout because everyone agrees that the constitution should be amended to change the way the president is elected", Hefni Kadri, a professor at Cairo's Ains Shams University, said.
Hassan Nafae, a political analyst in Cairo, added: "A low turnout would be a failure for the regime."