US-based charity World Central Kitchen, whose staff were killed in Monday night's drone strike, demanded that an independent commission investigate the killings.
Britain, which lost three nationals in the strike, called for a "wholly independent review."
Poland said it had demanded a "criminal inquiry" by Israel after what it called the "murder" of the aid workers, one of whom was Polish.
Israel said Friday it had been targeting a "Hamas gunman" in the strike, with the military admitting a series of "grave mistakes" and violations of its own rules of engagement.
FILE—This combination of photos provided by World Central Kitchen/WCK.org, shows seven aid workers who were killed in Gaza April 1, 2024.
Israel had announced earlier on Friday it would allow "temporary" aid deliveries into famine-threatened northern Gaza, hours after Washington warned of a sharp shift in its policy over Israel's war against Hamas.
Germany said Israel had "no more excuses" to delay the entry of aid, after nearly six months of war.
UN chief Antonio Guterres said "scattered measures" for Gaza aid were not enough. "We need a paradigm shift."
The toughened US position followed the killing of the World Central Kitchen workers—an Australian, three Britons, a North American, a Palestinian and a Pole.
An internal Israeli military inquiry found that the drone team had made an "operational misjudgement of the situation" after spotting a suspected Hamas gunman shooting from the top of an aid truck.
US Secretary of State Antony Blinken said it was "very important that Israel is taking full responsibility for this incident."
The UN chief said he was "deeply troubled" by reports in Israeli magazine +972 that the military was using artificial intelligence to identify targets in Gaza.
"No part of life and death decisions which impact entire families should be delegated to the cold calculation of algorithms," he said.
Extra aid route
In a tense, 30-minute phone call on Thursday, President Joe Biden told Prime Minister Benjamin Netanyahu that US policy on Israel was dependent on the protection of civilians and aid workers in Gaza, the first hint of possible conditions to Washington's military support.
Hours later Israel announced it would reopen another aid route into the Palestinian territory, which Israel placed under total siege after the war began.
"Israel will allow the temporary delivery of humanitarian aid" through the Israeli port of Ashdod and the Erez border crossing, as well as increased deliveries from Jordan at the Kerem Shalom crossing, Netanyahu's office said.
FILE— A view of Ashdod port after the Israeli cabinet approved the temporary use of the port for aid deliveries into Gaza, amid the ongoing conflict between Israel and Hamas, in Ashdod, Israel, April 5, 2024.
Biden said Israel was acting on the requests he had put to Netanyahu. "I asked them to do what they're doing," he said.
But European Council president Charles Michel said the measures announced by Israel were "not enough."
The bloodiest-ever Gaza war began with Hamas's October 7 attack that resulted in the deaths of 1,170 people, most of them civilians, according to an AFP tally of Israeli official figures.
Palestinian militants also took around 250 hostages, about 130 of whom remain in Gaza, including 34 the army says are dead.
Israel's retaliatory campaign has killed at least 33,091 people in Gaza, according to the Hamas-run territory's health ministry.
Efforts by Egyptian, Qatari and US mediators to broker a ceasefire and an exchange of hostages for prisoners have made no headway since a week-long truce in November.
CIA Director Bill Burns is to travel this weekend to Cairo where mediators will hold a new round of talks with Israel's spy chief David Barnea, the White House said.
'Insensitive'
Palestinians in northern Gaza have eaten an average of just 245 calories per day—less than a can of beans— since January, according to Oxfam.
UN agencies have accused Israel of blocking aid, but Israel has blamed shortages on aid groups' inability to distribute supplies once they get in.
Australian Foreign Minister Penny Wong told Britain's The Guardian newspaper that Netanyahu's initial comment on the aid workers' deaths was "deeply insensitive."
Netanyahu had said: "It happens in war" and said the killings were unintentional.
In his call with Netanyahu, Biden "made clear that US policy regarding Gaza will be determined by our assessment of Israel's immediate action" to improve the humanitarian situation, the White House said.
Allies have been pressing Biden to leverage the billions of dollars in US military aid.
Blinken told reporters: "If we don't see the changes that we need to see, there'll be changes in our own policy."
Wider tensions
In a call with his Israeli counterpart, Pentagon chief Lloyd Austin "discussed the threat posed by Iran and its proxy activities," the Israeli army said.
FILE—Mourners reach out to the flag-draped coffins of Revolutionary Guard members killed in an airstrike widely attributed to Israel that destroyed Iran's Consulate in Syria on Monday, in a funeral procession in Tehran, Iran, on April 5, 2024.
Iran blamed Israel for an air strike Monday on its consulate in Damascus that killed seven Iranian Revolutionary Guards, and has vowed retaliation.
Thousands of people chanted "death to Israel" at the funeral in Tehran on Friday.
Analysts saw the strike as an escalation of Israel's campaign against Iran and its regional proxies that runs the risk of triggering a wider war.
Israel said Thursday it was strengthening its defences and pausing leave for combat units following Iran's threats to retaliate.
Relentless Israeli bombardment has reduced much of Gaza to rubble, collapsed the hospital system and spawned a humanitarian crisis, with all of its 2.4 million residents "experiencing acute food insecurity and malnutrition," the World Bank has said.
Relief work has become almost impossible in Gaza, top global aid groups, including Oxfam and Save the Children, said after Israel killed the WCK staff.
A UN team finally reached Gaza's largest hospital Al-Shifa to assess the damage it sustained in a two-week Israeli military operation that destroyed many of its buildings and left scores dead.
"The loss to a health system already in tatters, amid skyrocketing health needs, is incalculable," said Ramesh Rajasingham of the UN humanitarian office (OCHA).