The two leaders are in Egypt, Kerry said, to "meet and discuss ways in which we might be able to bring about or encourage the parties to embrace a ceasefire under the right circumstances."
Israel and Hamas have been engaged in a deadly exchange of airstrikes for more than two weeks. Since Israel announced a ground operation last week, the Health Ministry in Gaza reported 583 Palestinian deaths, and the Israeli military reported 27 soldiers killed and two civilians.
While acknowledging Israel's right to self-defense, Kerry and Ban questioned the proportionality of the casualties.
"We are deeply concerned about the consequences of Israel's appropriate and legitimate effort to defend itself," Kerry stated.
"So many people have died," the secretary-general lamented, and the majority are civilians, women and children.
"While I understand all how, why Israelis has to respond militarily," said the U.N. head, adding the critical observation: "but there is a proportionality."
The two leaders are urging an immediate ceasefire.
Israel, Kerry pointed out, has accepted an Egyptian cease-fire proposal. "So only Hamas now needs to make the decision to spare innocent civilians from this violence."
Also on Tuesday, Kerry announced the U.S. has approved $47 million in aid to Gaza.