Story highlights Secretary of State John Kerry's comments were picked up in between interviews

He was talking to an aide about the situation in Gaza

It appears he was being critical of Israeli assurances of a precision military operation

The White House says Kerry heading to Egypt to pursue an end to the conflict

Secretary of State John Kerry raised eyebrows Sunday following comments, caught on an open mic, that left some wondering whether he was criticizing Israeli assurances that its ground offensive in Gaza would be limited.

Kerry's comments occurred between multiple television interviews. He was heard in a phone conversation with a State Department deputy, Jonathan Finer, discussing the deaths of Israeli soldiers killed overnight.

"I hope they don't think that's an invitation to go do more," Kerry said in the unguarded moment. "That better be the warning to them."

"It's a hell of a pinpoint operation. It's a hell of a pinpoint operation," Kerry said, a seemingly frustrated comment aimed at Israel.

"Right," Finer responded.

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Noting that the situation is "escalating," Finer added: "it just underscores the need for a cease fire."

"We've got to get over there," Kerry said, adding, "I think, Jon, we ought to go tonight. I think it's crazy to be sitting around. Let's go."

In a later interview with "Fox News Sunday," host Chris Wallace played the recording for Kerry.

"When you said 'It's a hell of a pinpoint operation,' are you upset that the Israelis are going too far?" Wallace asked. "And, in fact, do you intend to go back to the Middle East tonight, sir?"

"I think it's very, very difficult in these situations, obviously very difficult, Chris," Kerry replied.

"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 continued: "And so, yes, it's tough. It's tough to have this kind of operation. And I reacted obviously in a way that, you know, anybody does with respect to young children and civilians. But war is tough, and I said that publicly and I'll say it again. We defend Israel's right to do what it is doing in order to get at those tunnels."

The State Department said Kerry would travel to Cairo on Monday to meet with Egyptian and other officials about efforts to broker a cease-fire.