The Israel Defense Forces said Sunday it had "reached the seashore in the southern part of the city of Gaza and encircled the city of Gaza," calling the encirclement a "significant step" in the fight against Hamas.

"We will continue to attack strongly and continue to intensify our ground operation in the northern Gaza Strip and Greater Gaza City," the IDF said.

The IDF is still urging residents in northern Gaza to move south.

"We are intensifying our attack and this is already happening tonight significantly," the IDF warned.

Israeli Prime Minister Benjamin Netanyahu said Sunday at the Ramon Air Force Base in Israel that "there will be no cease-fire without the return of the hostages."

Israeli officials say 241 people have been taken hostage.

Secretary of State Antony Blinken traveled to Iraq to meet with Iraqi Prime Minister Mohammed Shia al-Sudani on Sunday following the secretary's visits to Israel, Jordan and the West Bank.

Blinken told reporters that his meeting with the Iraqi prime minister was productive and said he emphasized the need to prevent spillover from the conflict in Gaza.

"I made very clear that the attacks, the threats coming from militia that are aligned with Iran are totally unacceptable," Blinken said. "We're not looking for conflict with Iran. We've made that very clear. But we'll do what's necessary to protect our personnel."

"We're working very hard to make sure that the conflict in Gaza does not escalate, does not spread to other places, whether it's here, whether it's elsewhere in the region," he said.

Blinken was asked about Arab leaders' instance that nothing short of a total cease-fire would be acceptable.

"I think everyone would welcome humanitarian pauses -- there's no doubt about that," Blinken responded.

He said pauses "advance things that we're all trying to accomplish," including getting more humanitarian aid into Gaza, getting people out of Gaza and getting hostages home.

On his meeting with Palestinian Authority President Mahmoud Abbas, Blinken said the PA was "playing a very important role right now in the West Bank in trying to keep stability there."

-ABC News' Shannon Crawford

U.S. Secretary of State Antony Blinken visited the West Bank on Sunday, meeting Palestinian Authority President Mahmoud Abbas in an unannounced stop, the State Department said.

The two "discussed efforts to restore calm and stability in the West Bank, including the need to stop extremist violence against Palestinians and hold those accountable responsible," spokesperson Matthew Miller said in a statement.

President Joe Biden and Israeli Prime Minister Benjamin Netanyahu discussed Monday the possibility of "tactical pauses" in strikes on Gaza to help civilians reach safer locations, allow for more humanitarian aid to get in and help work toward the possibility of hostages being released, according to the White House.

"We consider ourselves at the beginning of this conversation, not at the end of it, so you can expect that we're going to continue to advocate for temporary vocalized pauses in the fighting," National Security Council spokesman John Kirby said.

He said less than 30 trucks of humanitarian assistance arrived in Gaza over the past 24 hours, which he said wasn't enough.

“In the early goings here, Israel was very resistant to humanitarian assistance getting in at all, and we persisted. We continue to persist," Kirby said. "Humanitarian aid is getting in, again, not to the degree we want it to, I'm not going to sugarcoat it. But, but, my goodness, based on our constant engagement, we've been able to make a big difference."

Kirby said "more Americans" will be leaving Gaza on Monday but he did not provide specific numbers.

Kirby said Biden and Netanyahu also discussed the situation in the West Bank and "reducing threats from terrorist groups that are operating there."

Kirby said their talks would continue and the leaders agreed to speak "in the coming day."

-ABC News' Justin Ryan Gomez