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.

The World Central Kitchen said it will resume operations in Gaza on Monday.

"The humanitarian situation in Gaza remains dire," CEO Erin Gore said Sunday in a press release. "We are restarting our operation with the same energy, dignity and focus on feeding as many people as possible. To date, we have distributed more than 43 million meals, and we are eager to deliver millions more."

"We will continue to get as much food into Gaza, including northern Gaza, as possible -- by land, air or sea," Gore added, in part.

Chef José Andrés' aid group had paused operations on April 2, when seven workers were killed in Gaza during an Israel Defense Forces drone strike, the food-relief organization has said.

Andrés, in an exclusive sit-down interview with "This Week" co-anchor Martha Raddatz earlier this month, said the strike is "unforgivable" and that Israel is committing a "war against humanity itself."

An investigation by the Israeli military into how the WCK strike occurred found that the decision to hit the aid convoy was a "serious violation" of their rules. It noted in its report the team that carried it out lacked sufficient evidence to do so, twice violating operating rules. In response, the IDF said it dismissed two officers, suspended two commanders and reprimanded three others. An Israeli military spokesman said it was "a terrible chain of errors, and it should never have happened."

Israeli officials have repeatedly defended their military operations in Gaza, insisting they take steps to curb civilian deaths while allowing aid to flow in that cannot benefit Hamas.