The Israel Defense Forces said 468 aid trucks entered Gaza on Tuesday -- the highest number to enter Gaza in one day since the war began.

More than 1,200 aid trucks have entered Gaza over the last three days, according to the IDF and Israeli aid agency COGAT.

Secretary of State Antony Blinken spoke emotionally Tuesday about the Americans directly impacted by the Israel-Hamas war, touching on both the hostages still held captive and the aid workers killed in Gaza.

At a news conference with his United Kingdom counterpart, David Cameron, Blinken was asked about Rachel Goldberg, whose 23-year-old son, American-Israeli Hersh Goldberg-Polin, was captured by Hamas. Goldberg is asserting that negotiators have failed.

"I know Rachel well. If I were sitting in her shoes, I'd undoubtably be feeling and saying the same thing," Blinken said. "Because until the day that Hersch is home, we will not have succeeded in doing what we're determined to do -- which is to bring him and bring all the hostages back."

Blinken also said he spoke with the family of Jacob Flickinger, a 33-year-old dual U.S.-Canadian citizen who was one of the seven World Central Kitchen aid workers killed by an Israeli strike in Gaza last week.

"I spoke over the weekend to Jacob's father and to his partner. I heard directly from them," he said. "Separately, Jacob leaves an 18-month-old son. Leaving everything else aside, just on a purely human level, my heart goes out to that family and to that little boy who now has no father."

-ABC News’ Shannon Crawford

Asked about Israeli Prime Minister Benjamin Netanyahu’s claim that Israel had set a date for its offensive in Rafah in southern Gaza, Secretary of State Antony Blinken told reporters Tuesday that the U.S. was in the dark. But Blinken added that he doesn't think the operation is imminent.

"No, we do not have a date for any Rafah operation -- at least one that's been communicated to us by the Israelis," Blinken said at a news conference with his United Kingdom counterpart, David Cameron. "On the contrary, what we have is an ongoing conversation with Israel about any Rafah operation. The president has been very clear about our concerns -- our deep concerns about Israel's ability to move civilians out of harm’s way."

Blinken said he expected talks between Israeli and American officials on the matter would press on into next week and that he didn’t want to "prejudge" an outcome.

"I don't anticipate any actions being taken before those talks," he said. "I don't see anything imminent."

As other Biden administration officials have done, Blinken stressed that the administration’s evaluation of Israel’s efforts to meet dire humanitarian needs in Gaza would be ongoing, and that officials would be "looking at a number of critical things that need to happen in the coming days."

Blinken said that list of items includes: opening a new portal for aid in northern Gaza; using Israel’s Port of Ashdod to bring in supplies on a regular basis; maximizing the flow of assistance from Jordan; repairing water lines throughout Gaza; and "putting in place a much more effective deconfliction mechanism with the humanitarian groups that are providing assistance."

-ABC News’ Shannon Crawford

Senate Minority Leader Mitch McConnell is claiming President Joe Biden is caving to political pressure on Israel.

McConnell criticized Biden for expressing outrage at the deaths of the seven World Central Kitchen aid workers, who were killed in an Israeli strike in Gaza last week, after his administration had called it a tragic accident.

"[That] begs the question whether he's also outraged at the way Israel's cherished aggressors violate international law by turning hospitals and schools [in Gaza] into fighting positions," McConnell said Tuesday. "Instead of welcoming Israel's swift investigation and efforts to hold personnel accountable for their mistakes -- accountability that has been sorely lacking during President Biden's own administration -- the president caved further to domestic political pressure. He indulged his radical base."

-ABC News’ John Parkinson

President Joe Biden called for an immediate cease-fire to get food and aid into Gaza in an interview airing Tuesday night on Univision.

"So I what I'm calling for is for the Israelis to just call for a cease-fire, allow for the next six, eight weeks total access to all food and medicine going into the country," Biden said in the interview with Univision's Enrique Acevedo. "I've spoken with everyone from the Saudis to the Jordanians to the Egyptians. They're prepared to move in. They're prepared to move this food in. And I think there's no excuse to not provide for the medical and the food needs of those people. It should be done now."

Biden did not mention tying the cease-fire to a hostage deal, according to a transcript of the interview, which would be a shift for the administration. ABC News has reached out to the White House for comment.

Last week, officials pushed back on suggestions that they were separating calls for a cease-fire from hostage negotiations in their readout of Biden's call with Israeli Prime Minister Benjamin Netanyahu.

"Our conviction remains that we need to see an immediate cease-fire to enable the release of hostages but also to enable a dramatic surge in humanitarian assistance, as well as obviously better protecting civilians," Secretary of State Antony Blinken said on April 4.

In the Univision interview, Biden also called Netanyahu's approach in Gaza "a mistake" when asked if he believed the prime minister was "more concerned about his political survival than he is in the national interest of his people" as calls for Netanyahu's resignation have increased following the strike that killed seven World Central Kitchen workers.

"Well, I will tell you, I think what he's doing is a mistake. I don't agree with his approach. I think it's outrageous that those four, three vehicles were hit by drones and taken out on a highway where it wasn't like it was along the shore, it wasn't like there was a convoy moving there, etc.," Biden said in the interview.

The hour-long interview, which is airing at 10 p.m. ET, was taped a day before Biden's call with Netanyahu on April 4.

-ABC News' Molly Nagle