Kerry was heard talking about Israeli soldiers killed in Gaza to a State Department official identified as Jonathan Finer just before appearing on the "Fox News Sunday" political talk show.
"I hope they don't think that's an invitation to go do more," Kerry says. "That better be the warning to them."
A frustrated Kerry then says: "It's a hell of a pinpoint operation, it's a hell of a pinpoint operation," in apparent frustration over the civilian toll in the Israeli operation.
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The Palestinian death toll topped 500 on Sunday as Israel pressed a ground offensive into the densely packed Gaza Strip after two weeks of aerial attacks.
"We've got to get over there," Kerry is heard saying on the Sunday recording. "I think, Jon, we ought to go tonight. I think it's crazy to be sitting around. Let's go."
When confronted over the remarks by Fox host Chris Wallace, Kerry reiterated Israel's right to self-defense.
"I think it's very, very difficult in these situations, obviously very difficult," Kerry said.
"You have people who've come out of tunnels. You have a right to go in and take out those tunnels. We completely support that. And we support Israel's right to defend itself against rockets that are continuing to come in. Hamas has started this process of rocketing, after Israel was trying to find the people who killed three young -- you know, one American kid, three young Israeli citizens. It's disgraceful," Kerry said.
"It's tough to have this kind of operation. I reacted obviously in a way that ... anybody does with respect to young children and civilians.
"But war is tough, and I've said that publicly and I've said it again. We defend Israel's right to do what it is doing in order to get at those tunnels," Kerry said.
Kerry then urged Hamas to "step up and be reasonable and understand that you accept the cease-fire, you save lives."
Kerry traveled to Cairo early Monday for crisis talks on Gaza, following President Barack Obama's call for an "immediate ceasefire" between Israelis and Palestinians in the conflict.
