A Rafah border crossing official said 632 foreign passport holders crossed from Gaza into Egypt on Thursday.

Twelve wounded Palestinians and 10 of their family members also crossed into Egypt on Thursday, the official said.

Several Congressional progressives continued calls for a cease-fire in Gaza while pushing back against a four-hour humanitarian pause.

"What we need is to stop the bombing," Rep. Cori Bush, D-Mo., said outside of the U.S. Capitol on Thursday during a press conference while joined by anti-war veterans in support of a cease-fire.

The event comes after National Security Council spokesperson John Kirby announced Thursday that Israel will start to implement four-hour pauses in fighting in areas of northern Gaza each day.

"Four hours? We don't want four hours. We don't want 16 hours. We don't want 22. We want a cease-fire now," Bush said.

Rep. Summer Lee, D-Pa., said a humanitarian pause does not account for the 2 million people stuck in Gaza.

"Any pause that doesn't take into account that this is still a collective punishment once the four hours has ended is not sufficient," Lee said.

-ABC News' John Parkinson and Lauren Peller

Israel will start to implement four-hour pauses in fighting in areas of northern Gaza each day, National Security Council spokesperson John Kirby announced Thursday.

"We've been told by the Israelis that there will be no military operations in these areas over the duration of the pause, and that this process is starting today," Kirby said.

Israel Defense Forces spokesman Richard Hecht said the pauses are already being held. Kirby said the pauses will be announced three hours ahead of time.

Kirby said these pauses are a "step in the right direction" and "significant first steps" to help civilians reach safer areas, away from the fighting.

"A four-hour pause for instance will allow, potentially, to move humanitarian assistance into that localized area, over that span of time. It could also provide enough of a window to help people get out of harm's way," Kirby said. "It could also provide brief windows of opportunity for safe passage for those hostages from where they're being held, to safer ground."

He said the Israelis have also agreed to a second humanitarian corridor that will allow people to leave hostile areas of northern Gaza.

"The second route along the coastal road will enable many more thousands to reach safer areas in the south," Kirby said. "Of course, we remain concerned that Hamas will discourage or prevent civilians from fleeing. At the same time, when encouraging people to leave areas of active operations, it's critical, absolutely vital, that humanitarian supplies and assistance are expanded in the areas where people are moving, in this case, southern Gaza."

Hecht, the IDF spokesman, stressed that it will only be "tactical, local pauses for humanitarian aid of a limited time and area," and the evacuation corridors would be for people to move south for humanitarian aid.

-ABC News' Justin Ryan Gomez

President Joe Biden confirmed that he has pressed Israeli Prime Minister Benjamin Netanyahu for a three-day pause in Gaza. Biden said he's also asked for an even bigger window to get the remaining hostages out.

Biden told reporters his message to the families of hostages is: "We're not going to stop until we get them out."

Israeli officials say Hamas had 239 hostages in Gaza. Four hostages were released from Gaza over the last few weeks: two American women and two Israeli women. The Israel Defense Forces said a fifth hostage, a female Israeli soldier, was rescued during the Israeli military's ground operations in Gaza.

Asked if there would be a cease-fire, Biden responded, "None. No possibility."

-ABC News' Justin Ryan Gomez and Tia Humphries

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