"Polygamy is often an injustice to women and children," said the influential cleric, in quotes published on Twitter late on Friday by Al-Azhar, Sunni Islam's most prestigious seat of learning.
The practice is the result of "a lack of understanding of the Quran and the tradition of the Prophet," he added.
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Tayeb also addressed the issue in a weekly Friday television show, telling viewers: "Those who say that marriage must be polygamous are all wrong".
He added the Koran says that in order for a Muslim man to have multiple wives, he "must obey conditions of fairness - and if there is not fairness it is forbidden to have multiple wives".
After the grand imam's comments sparked fervent debate on social media, Al-Azhar on Saturday clarified that he did not call for polygamy to be banned.
In his Friday comments, Tayeb called more broadly for the way women's issues are addressed to be revamped.
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"Women represent half of society, if we don't care for them it's like we are walking on one foot only," he said in the remarks published on Twitter.
The grand imam's approach was welcomed by Egypt's National Council for Women.
"The Muslim religion honours women - it brought justice and numerous rights which didn't exist before," said the Council's president Maya Morsi.
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