CAIRO—Egypt's military rulers will consider demands from secular parties that a constitution be drafted before elections are held, an official said, a move that could delay the country's first postrevolutionary polls and bolster non-Islamist political parties.

Military leaders would alter the timeline for Egypt's democratic transition if "political forces agreed on it," said Maj. Gen. Mohammed Assar, a member of the ruling military council, in a closed meeting with the American Chamber of Commerce in Egypt, according to the Chamber.

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