The developments come as tensions rise ahead of June 30, when Mursi marks one year in power as Egypt's first freely elected president following the 2011 uprising that toppled autocrat Hosni Mubarak.
In a four-page interview with the state-run Al-Ahram daily ahead of the anniversary, Morsi said demands for an early presidential vote are both "absurd and illegal."
He also warned against violence during upcoming demonstrations, which the opposition plans for the anniversary to demand his ouster.
The lengthy interview was a throwback to Mubarak's era when the paper served as a government mouthpiece, glorifying the regime's perceived successes and never challenging authorities.
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Before dawn today, attackers stormed and partially torched the downtown Cairo headquarters of a volunteer youth group, which has been gaining momentum lately and which is collecting signatures for Mursi's removal.
They hope for 15 million, believing the sheer number could push Mursi out of office by June 30. That's 2 million more than the number of votes Mursi garnered in last year's presidential election, which he won with 52 per cent of the votes. Egypt's population is around 90 million.