In a short recorded speech on Tuesday on state television, Mubarak said the referendum on Wednesday would be "a decisive moment in our contemporary history".
"I have full and unlimited confidence that you will turn out to take part, through the referendum, in making a new tomorrow for our country and exploring new and broad horizons in our political life," said Mubarak, who is expected to seek a fifth six-year term in contested elections in September.
Police in Cairo earlier on Tuesday dispersed a small demonstration against the constitutional amendment, which sets tough conditions for people who want to run for the presidency. It was by the liberal Ghad (Tomorrow) Party led by young lawyer Ayman Nour.
They also detained 15 more members of the opposition Muslim Brotherhood for questioning on charges they possessed leaflets calling for a boycott of the referendum. The Brotherhood says over 960 of its members are now in custody.
Nour led a demonstration against
the referendum on Tuesday
A broad coalition of opposition groups says the constitutional amendment will make little practical difference to political life because of the conditions for candidates who want to run against the ruling party.
For example, independents would need support from 65 of the 444 elected members of the People's Assembly or parliament, where the NDP has a 90% majority.
Recognised political parties face few restrictions this year but in any subsequent elections they can only field candidates if they hold 5% of parliamentary seats.
At a news conference in response, Nour called for a broad opposition alliance including the Muslim Brotherhood.
The government has tried to drive a wedge between Islamists and the secular opposition, analysts say. But Nour said: "We are in solidarity with our colleagues in the Muslim Brotherhood and in all organisations subject to direct political repression."
"I have full and unlimited confidence that you will turn out to take part..."
Meanwhile, in the northeastern town of Ismailiya, some 700 students staged a protest on Tuesday calling for a boycott of the referendum.
The students gathered at Ismailiya's Suez Canal University carrying banners against the referendum.
"Participating in the referendum means endorsing autocracy", "End the state of emergency" and "Free all detainees," the banners read.