For more of Wolf Blitzer's interview with Peres, tune into "Wolf" at 1 PM ET and "The Situation Room" at 5 PM ET.
Former Israeli President Shimon Peres left office only a week ago, yet it's already clear that his influence in the Israeli public sphere - and perhaps beyond - will remain significant.
He spoke with Wolf Blitzer on Thursday about the current conflict in Gaza, and how to go about finding a lasting peace between Israelis and Palestinians.
"I cannot see a cease-fire with rockets and with tunnels," Peres said. "Only a cease-fire without rockets and without tunnels."
Peres does not view Hamas as the legitimate political rulers of Gaza, referencing Hamas' coup of the territory in 2007.
He believes Gaza should be controlled by the Palestinian Authority, the ruling entity of the West Bank, and its president, Mahmoud Abbas.
"I don't think that two countries can bring peace," Peres said of a divided West Bank and Gaza. "Two countries will continue war."
Peres regards Abbas, or Abu Mazen, as he is known to Palestinians, as an essential figure in achieving Israel-Palestinian peace.
"He got the courage, more than any other Arab leader, to stand up and say, 'I'm against terror. I'm against kidnapping ... I'm for peace,'" Peres said.
I remember seeing footage of the horrible violence that erupted following elections in which Abbas's party initially looked like the winner in the territtory, and then later it shifted to Hamas – I seem to recall people getting thrown off buildings in the aftermath. Mr. Peres is a great man who commands respect worldwide. I wonder though if it is possible for Abbas to speak for Hamas supporters in a unified way following such a brutal breakup of the Palestinian territory into two major factions.
With all my heart i ask for peace between this to country, the leaders of these to nation must stop what ever they do th war the fight ,i want to ask something how can a man be show that he protect his citizen when women,children are dying bcoz of th huge ego of our leaders, how leaders think their mind ther are full of evil, to people of gaza im prayering with you , no innocent blood shall be split down & god be happy.be happy when your enemies ambark wall against you smash you down,be lyk the sand ,but i promise god wel speak4 u , i see dark cloud of isreal, i see red sky hanging over nation of isreal ,earth quakes, storm,natural disister, evry building wuld shaken ,if you dnt stop the killing of innocent child... My lord end war among th 2 nation ,bring peace to th people of this world