Tuesday's demonstrations have been called by largely secular opposition groups and Islamists backing Morsi.
He also tried to calm public anger by annulling a decree boosting his powers.
But some rulings of the 22 November decree - which stripped the judiciary of any right to challenge his decisions - will stand.
He had earlier called in the army to maintain security and protect state institutions ahead of Saturday's vote, granting it powers to arrest civilians.
The general prosecutor, who was dismissed, will not be reinstated, and the retrial of former regime officials will go ahead.
The opposition National Salvation Front has said it will not recognise the draft constitution, as it was drafted by an assembly dominated by Mr Morsi's Islamist allies.
On Monday evening, around 100 protesters milled around outside the presidential palace - a focus for earlier opposition demonstrations which the army has now surrounded with concrete blocks and ringed with tanks.
The president has said he is trying to safeguard the revolution that overthrew Hosni Mubarak last year, but critics calling for large turnouts at Tuesday's protest accuse him of acting like a dictator.
NSF chief co-ordinator Mohammed ElBaradei said the "sham" draft constitution defied Egyptians' "basic rights of freedom".
"It doesn't establish proper democratic systems, so at this stage at least we have decided that we are going to continue to fight tooth and nail against the referendum," the Nobel prize winner told the BBC's Newsnight programme.
Meanwhile, Mohamed Soudan, foreign relations secretary of the Muslim Brotherhood's Freedom and Justice Party, said Mr Morsi was constitutionally bound to go ahead with Saturday's vote because the date had been announced by the constituent assembly.
Mr ElBaradei would not go so far as to call for a boycott of Saturday's vote, but said he hoped the turn-out at Tuesday's protests would persuade Mr Morsi to postpone the referendum until consensus was reached through dialogue on a "proper, democratic" constitution.
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