Israel-Gaza updates: Israel says ground operation underway in southern Gaza

President Joe Biden touted the extension of the humanitarian pause in Gaza, saying in a new statement that he has "remained deeply engaged over the last few days to ensure that this deal -- brokered and sustained through extensive U.S. mediation and diplomacy -- can continue to deliver results."

Fifty-eight hostages -- 40 Israelis and 18 foreign citizens -- have been released so far, including 4-year-old American-Israeli Abigail Idan. Abigail was released on Sunday, two days after her 4th birthday.

Biden said he "spoke with Abigail’s family following her release, and we are working closely with our Israeli partners to ensure she gets the care and support she needs as she begins to recover from this unspeakable trauma."

Biden also noted, "We are taking full advantage of the pause in fighting to increase the amount of humanitarian aid moving into Gaza, and we will continue our efforts to build a future of peace and dignity for the Palestinian people."

The president thanked leaders from Israel, Qatar and Egypt for their continued work, and vowed, "We will not stop until all of the hostages held by Hamas terrorists are released."

-ABC News' Molly Nagle

While the cease-fire extension is expected to bring the release of additional hostages, National Security Council spokesperson John Kirby acknowledged there's a "real risk" that Hamas could benefit the longer the cease-fire continues.

"Without getting into intelligence issues," Kirby said, "any pause in the fighting could benefit your enemy in terms of time to refit, to rest your fighters, to rearm them, reequip them."

Kirby said the cease-fire is a "calculated risk" that Israeli Prime Minister Benjamin Netanyahu is willing to take to get hostages out, and that military operations will resume against Hamas leadership.

-ABC News' Molly Nagle

The U.S. believes there are eight or nine Americans still being held in Gaza, National Security Council spokesperson John Kirby said, adding that the U.S. does not have "solid information on each and every one of them."

Asked if Americans were expected to be released in the coming days, Kirby said the administration "certainly hope[s] so," but did not say more.

"I mean, we're going to watch this very, very closely. We're certainly hoping that another batch of hostages gets released today as part of the fourth and final day of the original agreement. We’re going to be watching closely to see if any Americans are in that group," Kirby said.

"We don't really know until you get into the end game who's going to be actually on that list and then, even then, you got to watch closely [to see] if who's on the list is folks that actually come out," he said.

Kirby was asked specifically about the two American women who were expected to be part of the first round of releases, and he reiterated his hope they would be released Monday.

-ABC News' Molly Nagle

Hamas officials said they've received a list of Palestinian prisoners who are expected to be released from Israel on Monday in exchange for hostages. The list includes three women and 30 children, Hamas officials said.