The Israel Defense Forces announced that it has “completed operational activity in the area of Khan Younis” in the southern Gaza Strip on Tuesday morning, more than a week after it began bombarding the eastern part of the city -- a designated humanitarian zone.

At least 226 people have been killed by Israeli forces in and around Khan Younis since the IDF raid began early on July 22, according to Gaza’s Hamas-run Ministry of Health.

-ABC News' Diaa Ostaz, Jordana Miller and Samy Zyara

At least one person is dead in northern Israel following a rocket salvo from Lebanon this afternoon, according to Israel’s national emergency service. One person was also killed in southern Lebanon following a drone strike targeting a house in the town of Beit Lif early Tuesday, according to Lebanon's National News Agency.

The Israel Defense Forces said its fighter jets conducted strikes in southern Lebanon earlier Tuesday.

Approximately 10 projectiles crossed from Lebanon into Israeli territory, with the majority of the projectiles being intercepted, according to the IDF. A direct hit was identified in the area of HaGoshrim in northern Israel.

U.S. officials’ meetings with Israeli Prime Minister Netanyahu in Washington, D.C., last week were "very constructive and certainly nothing that discouraged us in terms of trying to close the remaining gaps" while trying to secure the hostage deal, National Security Council spokesman John Kirby told reporters Monday.

"We still believe those gaps can be narrowed ... and we can move forward. But obviously, as I said earlier, it's going to take compromise, it's going to take leadership," he said.

"There's no indication that we see, at this point in time, the weekend strike by Hezbollah into the Golan [Heights] area is going to negatively affect those discussions," Kirby added.

Kirby also pushed back on the suggestion that Vice President Kamala Harris had a different message for Netanyahu from President Joe Biden, saying there was "no daylight" between their messages, and that reporting suggesting otherwise was "unfortunate and inaccurate."

"There was no daylight between anything, the president, the vice president told the prime minister. Same points, same emphasis -- the commitment and reaffirmation to help Israel continue to defend itself against these threats. Same reaffirmation by both the president and the vice president, that we want to see the cease-fire deal get enacted because of what it can do to improve the humanitarian situation. And of course, getting those hostages home with their families," Kirby said.

Pressed on why Harris had her own meeting if their message was the same, Kirby defended Harris.

"The vice president couldn't be in town for the meeting in the Oval [Office], and as she has been a full partner in all our foreign policy, but certainly in particular, the policy that this administration has pursued with respect to the Middle East, she felt it was important to also sit down with Prime Minister Netanyahu,” Kirby said.

-ABC News’ Molly Nagle

The United States "absolutely condemn this weekend's horrific attack" that killed children playing soccer in Majdal Shams in the Israeli-controlled Golan Heights, National Security Council spokesman John Kirby told reporters Monday.

At least 12 people were killed, according to the Israel Defense Forces. Hezbollah has denied involvement in the rocket attack but Secretary of State Antony Blinken said Sunday that "every indication" points to Hezbollah as responsible for the strike.

Kirby also assigned blame to Hezbollah in Lebanon, saying "it was their rocket launched from an area that they control."

"The United States will continue to support efforts to reach a diplomatic solution along that blue line that will, No. 1, end these terrible attacks once and for all, and No. 2, allow Israeli and Lebanese citizens on both sides of the border to safely return to their homes," Kirby said.

Kirby stressed that U.S. support for Israeli security remains "ironclad" against all Iran-backed threats, adding, "We believe that there is still time and space for a diplomatic solution."

Asked if the administration was urging Israel to show restraint in any response, Kirby said that Hezbollah made the first strike on Israel back in October and that "Israel has every right to respond," but he said he was confident that a broader conflict could be avoided.

"Nobody wants a broader war and I'm confident that we'll be able to avoid such an outcome. I'll let the Israelis really speak to whatever their response is going to be," Kirby said.

-ABC News’ Molly Nagle