Benjamin Netanyahu claimed on Tuesday that Israel’s month-long offensive against Hamas in Gaza was an “extraordinary success” as Israeli troops began operating inside Gaza City, the besieged strip’s capital.

Speaking to soldiers in a televised speech, Israel’s prime minister said there were “problems” with drones, improvised explosive devices and anti-tank fire and sometimes “very painful losses”.

But he added that “all in all, the success is phenomenal because we went in there and hit the enemy”.

“We do not intend to stop. We intend to continue to the end,” he said.

His comments came as Israeli forces embarked on the most challenging phase of their offensive in Gaza — urban combat in Gaza City, the heart of Hamas’s operations in the northern area of the strip.

After encircling the city this week, defence minister Yoav Gallant said on Tuesday that Israeli forces were now operating in “built-up” areas.

“Our forces from the north and the south are advancing to the heart of Gaza City,” Gallant said. “They are operating in built-up areas (of the city).”

Israeli forces mounted the offensive on the coastal enclave after Hamas, which controls Gaza, launched a deadly attack in southern Israel that killed more than 1,400 people, according to Israeli officials. The Islamist militant group also seized more than 240 hostages.

As Israel has laid siege to the strip and bombarded it with air and artillery strikes, more than 10,000 people have been killed in Gaza, according to Palestinian officials.

Israel has ordered Palestinians to move from the north to the south as more than 1mn people — half the population — have been displaced.

Gallant called again on Gazan citizens who still remained in the north of the strip to move south, saying that “thousands” were leaving.

Netanyahu told ABC News on Monday that Israel would maintain an indefinite grip over Gaza, which is home to 2.3mn Palestinians, to ensure its own security. It was his first explicit comments on the country’s plans for the Palestinian enclave after its war with Hamas.

The Gaza Strip should be governed by “those who don’t want to continue the way of Hamas”, Netanyahu said, without clarifying whether he was referring to the Palestinian Authority, a rival to the militant group, or an international force.

“I think Israel, for an indefinite period, will have the overall security responsibility because we’ve seen what happens when we don’t have it.”

Netanyahu’s comments reflect changing Israeli policy amid concerns among foreign diplomats about whether Israel has a clear plan about what will happen once the fighting stops.

In October, Gallant said Israel would no longer have “responsibility for life in the Gaza Strip” once the war was over. He added that the conflict would create “a new security reality” for Israeli citizens.

At a meeting of G7 foreign ministers in Tokyo on Tuesday, UK foreign secretary James Cleverly said: “At some point in the future I think the world would want to see a Palestinian leadership as part of that route towards a sustainable, peaceful two-state solution.

“But at some point after the immediate conflict and before the creation of civilian leadership, it is inevitable that the military forces on the ground would have to take over security control.”

Arab diplomats last week dismissed US efforts, led by secretary of state Antony Blinken, to rally regional support for the PA, which administers parts of the occupied West Bank, as premature. The group was ousted from Gaza in 2007 after losing elections to Hamas.

Netanyahu told ABC that he would be in favour of tactical pauses, especially to help free some of the 242 hostages held by Hamas, but he has repeatedly rejected the broader ceasefire demanded by Arab leaders, the UN and other international organisations.

“As far as tactical little pauses, an hour here, an hour there — we’ve had them before,” he said. “We’ll check the circumstances in order to enable goods, humanitarian goods to come in, or our hostages, individual hostages to leave.”

In a phone call on Monday, US president Joe Biden pressed Netanyahu to agree to “temporary local pauses”, said John Kirby, US National Security Council spokesperson.

“This remains something we are actively discussing with our Israeli counterparts and we consider ourselves at the beginning of this conversation, not at the end of it,” Kirby said.

The US administration does not support a full ceasefire, which it says would only give Hamas time to regroup.

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Israel has tightly restricted the entry of humanitarian aid into Gaza, down from more than 400 trucks a day before the war to a few dozen a day. International observers have warned that these curbs are deepening a humanitarian crisis.

Just over 500 trucks have been allowed to cross into Israel from Egypt since the beginning of the war, with another 75 scheduled to have crossed on Monday, according to an Israeli military assessment.

Diplomats have also been racing to ensure that the Rafah crossing with Egypt remains open for foreign nationals trying to flee the war, but disagreements between Israel, Egypt and Hamas on who will be allowed out have disrupted the process.

An Israeli air strike on a convoy of ambulances heading to Rafah, the only crossing not controlled by Israel, has also caused delays. Israel said one of the ambulances was carrying a Hamas militant.

Additional reporting by David Keohane