Israel has dramatically increased the flow of humanitarian supplies into Gaza, allowing on average 200 aid trucks a day, with some days as many as 400 trucks getting through, according to a top U.S. official.

Now, the focus needs to move beyond "counting trucks" and instead look to ensure the right supplies are being distributed throughout Gaza, according to David Satterfield, the State Department’s special envoy for Middle East humanitarian issues.

"Our first priority was -- because it had to be -- averting famine," Satterfield told reporters on Tuesday. "But we now need to move on beyond that goal to addressing the true needs: sanitation, availability of medicines, availability of potable water, the specialized care required for these vulnerable populations."

The United Nations this week is conducting a more detailed assessment on the needs for the civilian population, Satterfield said.

He said the U.N. needs more trucks that are cleared by the Israeli military to operate inside Gaza. He also said the Erez crossing between Gaza and Israel and an additional northern crossing must become accessible.

"Our work is focused every day, every hour, on seeing continuous progress made," he said.

-ABC News’ Anne Flaherty

The Israel Defense Forces has denied accusations from the Hamas-run Gaza Health Ministry that they buried at least 283 bodies in a mass grave near Nasser Hospital in Gaza.

"The claim that the IDF buried Palestinian bodies is baseless and unfounded," the IDF said in a statement. "During the IDF’s operation in the area of Nasser Hospital, in accordance to the effort to locate hostages and missing persons, corpses buried by Palestinians in the area of Nasser Hospital were examined."

"The examination was conducted in a careful manner and exclusively in places where intelligence indicated the possible presence of hostages," the IDF said. "Bodies examined, which did not belong to Israeli hostages, were returned to their place."

White House national security communications adviser John Kirby said Tuesday that the reports of mass graves are "deeply concerning," but the White House is not in a place to validate the reports.

"I wouldn't expect a U.S. investigation," Kirby said, adding, "We'll certainly talk to our Israeli counterparts."

Israel's Ambassador to the United Nations, Gilad Erdan, is claiming that more than 2,135 workers at UNRWA, the U.N. agency for Palestinian refugees, are members of Hamas or the Palestinian Islamic Jihad.

"Hamas has infiltrated UNRWA so deeply that it is no longer possible to determine where UNRWA ends and where Hamas begins," Erdan said. "Israel calls on the donor countries to refrain from transferring their taxpayers' money to UNRWA-Gaza, as these funds will go to the Hamas terrorist organization, and that violates legislation in the donor countries themselves."

This comes after an independent review of UNRWA released on Monday found the agency had policies in place to back up its principle of neutrality, but also found UNRWA had "serious gaps in implementation," The Associated Press reported. The report made recommendations to improve the agency’s neutrality.

The report also found that Israel hadn’t provided evidence to back up its claim that a significant number of UNRWA employees were members of Hamas or PIJ, the AP said.

Iranian Foreign Ministry spokesman Nasser Kanaani called Israel’s retaliatory strike against Iran last week "harassment" that has "caused no damage whatsoever."

"In our opinion, this issue is not worthy of addressing," Kanaani said Monday.

A video released by Hamas on Telegram Saturday features two men who identify themselves as hostages captured on Oct. 7.

The heavily edited video cuts between the two men -- who identify themselves as American citizen Keith Siegel, 64, and Israeli citizen Omri Miran, 47, from Kibbutz Nahal Oz -- as they speak to the camera under duress.

The men express how much they miss their families and their sadness at missing Passover celebrations. They also ask their families to continue to pressure the Israeli government for a deal.

"I want to tell my family that I love you very much," Siegel says in the video.

"I have very, very beautiful memories of Passover last year when we all celebrated together, and I really hope we all have the best surprise possible," he says, before bursting into tears.

ABC News has not independently verified where or when the video was filmed, though in the video Miran says he has been in captivity for more than 202 days. Saturday marks 203 days since Hamas' Oct. 7 attack.

Siegel's wife, Aviva Siegel, was also taken hostage and released during the first cease-fire and hostage deal.

In a video message released on Saturday in response to the Hamas video, his wife said, "Keith, I love you, we will fight until you return."

She was joined in the video by the couple's two daughters.

"Seeing my father today only emphasizes to all of us how much we must reach a deal as soon as possible and bring everyone home," their daughter, Ilan Siegel, said. "I demand that the leaders of this country watch this video and see their father crying out for help."

The Hostage and Missing Families Forum said in a statement following the release of the latest video that the "proof of life from Keith Siegel and Omri Miran is the clearest evidence that the Israeli government must do everything to approve a deal for the return of all the hostages before Independence Day."

"Now is the time for the government and its leader to prove through actions their commitment to the citizens of Israel who await the return of the hostages," the statement continued. "The Israeli government must not miss this opportunity to bring them all home!"

The Israeli government did not immediately respond to ABC News' request for comment on the video.

The video comes three days after the release by Hamas of a video showing a man who identified himself as Hersh Goldberg-Polin, a 24-year-old American who was captured at the Nova Music Festival on Oct. 7.