President Donald Trump acknowledged Israel's renewed airstrikes in Gaza on Wednesday, though said he believed phase one of the current ceasefire would hold and that phase two would come to fruition.

"You know, they had a problem today, I understand, with a bomb that went off," Trump told reporters. "Hurt some people pretty badly, probably killed some people, they're telling me, it just happened."

The airstrikes came after four Israeli troops were injured in what the Israel Defense Forces said was a Hamas attack in the southern Gaza city of Rafah. At least five people were killed in the retaliatory Israeli strikes, the Kuwait field hospital in southern Gaza reported.

Nonetheless, Trump said that he believed the ceasefire -- which came into effect in October -- was "going along well."

Trump also expressed confidence in the implementation of phase two of the agreement. "Phase two is moving along, yeah. It's going to happen," he said.

-ABC News' Isabella Murray, Nicholas Kerr, Hannah Demissie, Michelle Stoddart, Selina Wang and Meghan Mistry

Israeli forces said in a statement that they struck an alleged "Hamas terrorist" in the southern Gaza Strip on Wednesday.

At least five people were killed and 10 people were injured by the Israeli strikes, the Kuwait field hospital in southern Gaza reported.

The Israel Defense Forces said the strikes were in response to what it called a "blatant violation" of the ceasefire agreement earlier in the day. In that incident, four IDF soldiers were injured after an exchange of fire in Rafah.

-ABC News' Jordana Miller and Diaa Ostaz

At least seven people were injured at a school where displaced people are living in Gaza City after it was targeted by Israeli fire on Tuesday, according to the Gaza Civil Defense and Al-Ahli Arab Hospital in Gaza City.

The school is located in a part of Gaza that Israeli troops are not in control of, past the yellow line established in the first phase of the ceasefire.

When asked about the incident, the Israel Defense Forces said troops identified “suspicious movement,” while “operating in the northern Gaza Strip,” in a statement to ABC News.

IDF troops “fired to remove the threat” in the area, and details of the incident are “under review,” the IDF said.

-ABC News' Jordana Miller and Diaa Ostaz

Four Isreal Defense Forces soldiers were wounded after Hamas members “carried out an attack against IDF troops operating in eastern Rafah,” in an area in Gaza that is under Israeli control, an Israeli military official told ABC News.

The Hamas members “opened fire and used heavy weapons against” IDF troops, the military official said.

IDF troops “returned fire in response to the attack,” the military official added.

The Israeli military official called this incident “another clear violation of the ceasefire agreement.”

Israeli Prime Minister Benjamin Netanyahu said Israel will respond to the attack "accordingly."

-ABC News Jordana Miller