"We targeted only the second floor, which is where the senior terrorists were," the IDF said on Twitter, adding that reporters had been used as human shields. "The rest of the building was unharmed. Direct hit confirmed."

Calls for a truce came on the heels of the single deadliest attack -- an Israeli airstrike in Gaza City on Sunday that left a family of 10 dead within a building's broken concrete and mangled metal.

Al Qassam Brigades, Hamas' military arm, called it a "massacre committed by Israeli occupation" on Twitter.

The Israeli airstrike targeted Yehya Bayaa, "a senior Hamas member," said Lt. Col. Avital Leibovich, the Israel Defense Forces' chief spokeswoman. The IDF alleges Bayaa is one of the leaders of a Hamas rocket-launching unit.

As it's happening: CNN reports on the ground

The building hit was a known hiding place for Bayaa -- though not his home, as was reported earlier -- Leibovich said. Initially, the IDF reported it killed Bayaa in the attack. But late Sunday, Leibovich said she did not know for sure whether Bayaa had been killed.

Israeli military Capt. Eytan Muchman added Monday that, "very regrettably," the Dallo family was inside the building. Regev later told CNN's Anderson Cooper, "Obviously, it was a foul-up" -- saying that while Israel doesn't know exactly what happened and believes Hamas is using civilians as human shields, it is "a failure" every time an innocent bystander is killed.

That same day, hundreds gathered at the al-Isra mosque for a funeral of some family members killed, CNN's Ben Wedeman reported.

The firing of rockets before and after the funeral didn't deter some mourners.

"Revenge, revenge," they chanted.

Talking Monday night with CNN's Piers Morgan, Peres insisted Israel has nothing against people in Gaza or Muslims, in general. He said his country's aim -- and the only reason it launched its military offensive -- is to keep its own citizens safe.

"We don't hate them. We don't try to get any glories," the Israeli president said. "We want to live in peace."