The developments come as tensions rise ahead of June 30, when Morsi 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.
"Violating the law, the use of violence or inciting for it are unacceptable and will not be permitted," Morsi told the paper on Friday. "We are in a country with a constitution and law. We had free and fair elections and the talk about early presidential elections is absurd and illegal."
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.
Before dawn Friday, 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 Morsi's removal.
The drive, known as "Tamarod" or "Rebel" in Arabic, is helping galvanize an opposition that has long been in disarray and demoralized. So far, the volunteers say they have collected about 7 million signatures.
They hope for 15 million, believing the sheer number could push Morsi out of office by June 30. That's 2 million more than the number of votes Morsi garnered in last year's presidential election, which he won with 52 percent of the votes. Egypt's population is around 90 million.
The volunteer group said it received threats prior to the 3:30 a.m. attack, alerting some activists to stay overnight at the office.
"We were awakened by someone trying to break the door and the glass and then we saw fire under the door, coming at us," said Hassan Shahine, one of the campaign founders.
Shahine, who suffered light burns trying to extinguish the fire, blamed Morsi's Muslim Brotherhood for the attack, saying the president's party is "the only one who would think of doing this." The volunteers filed a police complaint against Brotherhood leaders after the attack, he added.
A Brotherhood spokesman, Mourad Aly, dismissed the accusations, saying the group has no reason to "burn the office of a group (of activists) as weak as this."
During Morsi's tumultuous year in power, Egypt has witnessed deadly bouts of violence and mass street protests while the country's economy plummeted and security woes only worsened.
Egypt's liberal and secular-minded opposition accuses Morsi and the Brotherhood of causing deep polarization among Egyptians. It says the president has not fulfilled his promises of creating an inclusive political process and instead has been enabling his Brotherhood to monopolize power.
For their part, Morsi and the Brotherhood say the opposition has no grass-root support and after failing in the elections, wants to unseat the president through street protests and violence.
Over the past months, the anti-Morsi petition has involved thousands of volunteers hitting the streets across the nation, passing out forms calling for Morsi to step down to anyone who wants to sign on.
On several occasions, the volunteers were attacked, allegedly by Morsi's supporters.
The campaign has also provoked a counter-drive, called "Tajarod" or "Impartiality," which has gathered millions of signatures in Morsi's support.
At the Cairo offices of the anti-Morsi petition, the front door and the ceiling were blackened from the fire and ashes covered the floor Friday but the group pledged to press on with its campaign.
"We are holding on to our pacifism, we are a peaceful campaign," said activist Mai Wahba, adding that the attack "will only strengthen the opposition."
The petition has no legal force, which underscores the campaign's limitations but the opposition highly depends on the size of the upcoming anniversary protests to give weight to their call.
The organizers say once they have 15 million signatures, they will take the petition to the Supreme Constitutional Court to seek new elections, though there's no basis for this under the country's newly adopted constitution.
Morsi has three more years to his term.