Multitalented artist Winnie Khumalo hopes her health will improve when she goes under the knife in J.
"Once again, the people of Israel and Palestine are embroiled in a deadly contest of tit-for-tat violence in which there can never be victors, only losers," Tutu said in a statement.
"Like children following a playground dust-up, political and religious leaders fall over each other, not to make peace, but to proclaim: It wasn't us, they started it."
He said Israel would never achieve true security and safety through oppressing the Palestinians, and Palestine would never achieve peaceful self-determination through violence.
"No conflict is intractable; no disagreement so absolute that it can never be healed.
"The world is looking to Israelis and Palestinians to be bigger than themselves; to act now, before any more children are harmed," said Tutu.
Scores of people have died during two days of Gaza raids.
According to Agence France-Presse, 11 women and children were among 17 Palestinians killed in Israeli strikes on Wednesday.
This brought the death toll to 38 in two days, according to the report.
More than 300 people have been wounded.