The White House maintained Tuesday that it doesn't believe Israeli forces should reoccupy Gaza following Israeli Prime Minister Benjamin Netanyahu's comments that the country will have the "overall security responsibility" in Gaza for an "indefinite period" after the war ends. "The president still believes that a reoccupation of Gaza by Israeli forces is not good. It's not good for Israel; not good for the Israeli people," said National Security Council coordinator for strategic communications John Kirby on "CNN This Morning." "One of the conversations that Secretary (Antony) Blinken has been having in the region is what does post-conflict Gaza look like? What does governance look like in Gaza? Because whatever it is it can't be what it was on October 6. It can't be Hamas," he added. The latest warning from the White House comes after Netanyahu told ABC News on Monday that Gaza should be governed by "those who don't want to continue the way of Hamas" before adding, "I think Israel will, for an indefinite period, will have the overall security responsibility because we've seen what happens when we don't have it." It was one of the first hints Netanyahu has given about his vision for a post-war Gaza and suggests a divergent view than that of the US, including President Joe Biden's own statements about what the future of the strip would look like. Mark Regev, a senior adviser to Netanyahu, told CNN's Christiane Amanpour on Tuesday that Israel's post-war plan is not an "ongoing occupation" of Gaza. "I think you could expect something more fluid, something more flexible where we can move in and move out as need be to deal with the security situation," he said. "We're not talking about any sort of ongoing occupation of the Gaza strip." Asked about Netanyahu's comments on ABC News on Monday that Israel will have the "overall security responsibility" in Gaza for an "indefinite period" after the war ends, Regev said: "We have to distinguish between a security presence and political control." "When this is over and we have defeated Hamas, it is crucial that there won't be a resurgent terrorist element, a resurgent Hamas. There is no point doing this and just going back to square one," Regev told CNN. "There will have to be an Israeli security presence, but that doesn't mean Israel is re-occupying Gaza, that doesn't mean that Israel is there to govern the Gazans," he continued. "On the contrary, we are interested in establishing new frameworks, where the Gazans can rule themselves, where there can be international support for the reconstruction of Gaza. Hopefully, we can bring in countries – Arab countries as well – for a reconstruction of a demilitarized, post-Hamas Gaza," he said. Netanyahu on Tuesday said "Gaza City is encircled" and the Israel Defense Forces are "operating in it" and "advancing the pressure applied on Hamas every hour and every day." It's unclear based on comments from Netanyahu and Israeli Defense Minister Yoav Gallant — who said that troops are at the "heart of Gaza City" — exactly where the IDF is operating inside Gaza. "So far, we've killed thousands of terrorists, from above and under the ground," Netanyahu said in a press conference. "Hamas is finding out that we're getting to places it didn't think we'd reach. And the campaign is still underway." "On the diplomatic front, we're operating around the clock to allow the IDF the leeway for the remaining military operation," Netanyahu added. "We will not stop until the victory." Netanyahu also warned Hezbollah against entering the war on Israel's northern front. "We will not comply with a reality in which Hezbollah or Hamas in Lebanon will hurt our communities and civilians. We'll continue responding with fierce fire against any attack," Netanyahu said. "If Hezbollah chooses to enter the war, this will be the biggest mistake in its life." Netanyahu added that he is in "constant touch" with US President Joe Biden, saying, "We highly appreciate his support and of the American administration and people." — CNN