Next week's second round is likely to give another "yes" vote as it includes districts seen as more sympathetic towards Islamists, analysts say, meaning the constitution would be approved.
But a close win would give Islamist President Mohamed Morsi only limited cause for celebration by showing the wide rifts in a country where he needs to build consensus on tough economic reforms. The Muslim Brotherhood's party, which propelled Morsi to office in a June election, said 56.5 percent backed the text. Official results are not expected till after the next round.
While an opposition official conceded the "yes" camp appeared to have won the first round, the opposition National Salvation Front said it did not acknowledge unofficial results.