Remains of American Israeli hostage among 3 bodies returned by Hamas, IDF says

President Donald Trump said he backs Israel's strikes on Gaza, arguing the move was "retribution" for a reported attack on Israeli troops -- but he's said he's confident the ceasefire deal will hold.

Trump said "Israel should hit back" following strikes on Gaza after Israel accused Hamas of violating the ceasefire agreement.

Still, the president remained confident that the ceasefire would hold, repeating his threat that if Hamas is "not good, they’re going to be terminated."

"Nothing's going to jeopardize that," Trump said, referring to the ceasefire. "You have to understand, Hamas is a very small part of peace in the Middle East, and they have to behave. They're on the rough side, but they said they would be good. And if they're good, they're going to be happy, and if they're not good, they're going to be terminated. Their lives will be terminated. And they understand that."

He added, "If we have to, we'll take out Hamas very easily, and that'll be the end of Hamas. We would rather not. We made a deal with them where they were going to behave, and they have to behave. If they don't behave, they get taken out."

-ABC News' Lalee Ibssa

The International Committee of the Red Cross called Hamas' alleged staging of the discovery of a body in Gaza while Red Cross observers were in attendance on Monday "unacceptable."

The Israel Defense Forces released a video that it said shows Hamas staging the discovery of a hostage body in Gaza.

"It is unacceptable that a fake recovery was staged, when so much depends on this agreement being upheld and when so many families are still anxiously awaiting news of their loved ones," the ICRC said in the statement on Tuesday.

ICRC observers accompanied Hamas earlier this week to provide any needed technical guidance in recovery efforts, but the ICRC does not participate in searching for the deceased or in physical recovery of remains per international law.

"The ICRC is raising its concerns directly with the parties," the organization added.

Israeli authorities cited this as one of the reasons for conducting strikes in Gaza on Tuesday, threatening the fragile ceasefire in place.

-ABC News' Cindy Smith

Hamas said it had "no connection" to the shooting incident in Gaza earlier Tuesday, in a statement.

This is the incident Israeli authorities said led to the decision for Israeli forces to conduct strikes in Gaza on Tuesday.

Hamas called Israel's decision to strike parts of Gaza on Tuesday a "blatant violation" of the ceasefire agreement," and said it was one of a "series of violations" committed by Israel in recent days.

Hamas added they are committed to the ceasefire and called on mediators to take "immediate action" to pressure Israel to adhere to the terms of the agreement.

-ABC News' Diaa Ostaz

Israeli Prime Minister Benjamin Netanyahu made the decision to conduct strikes in Gaza with the Israeli Defense Forces and then informed President Donald Trump before the action was taken, an Israeli official and a U.S. official confirmed to ABC News.

-ABC News' Jordana Miller and Anne Flaherty