• Abu Aqla, 51, died while covering a raid by Israeli forces in the occupied West Bank. Her producer was injured.
• Al Jazeera said Israeli troops "deliberately" shot her. Israel's prime minister said it was "likely" she was shot by Palestinian gunmen.
UN Secretary General António Guterres says he is "appalled" by Wednesday's killing of veteran Palestinian-American Al Jazeera journalist Shireen Abu Aqla.
The US also condemned the killing and called her a "reporting legend".
Abu Aqla, 51, died while covering a raid by Israeli forces in the occupied West Bank. Her producer was injured.
Al Jazeera said Israeli troops "deliberately" shot her. Israel's prime minister said it was "likely" she was shot by Palestinian gunmen.
But Naftali Bennett's military chief said the Israeli armed forces were not yet able to determine what happened.
Palestinian Authority President Mahmoud Abbas said he held the Israeli government fully responsible for what he described as a "crime of execution".
In a statement issued via his spokesperson late on Wednesday, Mr Guterres called on "the relevant authorities to carry out an independent and transparent investigation into this incident and ensure that those responsible are held accountable.
"The secretary general condemns all attacks and killings of journalists and stresses that journalists must never be the target of violence," the statement added.
Meanwhile, White House spokeswoman Jen Psaki wrote on Twitter that Americans were "heartbroken to learn of the killing" of Abu Aqla and the injuries to her producer.
"We send our deepest condolences to her family, friends, and strongly condemn her killing," Ms Psaki added, calling her a "reporting legend" who will be "mourned by all who knew her".
Abu Aqla was widely known and widely admired - by viewers and colleagues alike.
Early on Wednesday morning she went to the Jenin refugee camp to report on a raid by Israeli soldiers and security forces, which the Israeli military said was conducted to apprehend "terrorist suspects".
"During the activity, tens of Palestinian gunmen fired at and hurled explosive devices toward the soldiers. The soldiers responded with fire toward the gunmen and hits were identified," a military statement said.
The Palestinian health ministry said Abu Aqla was hit in the head by a live bullet during the raid. She was taken to hospital in a critical condition and later pronounced dead.
Another Palestinian journalist, Al Jazeera producer Ali Samoudi, was shot in the back and was in a stable condition in hospital, the health ministry added.
"We were going to film the Israeli army operation and suddenly they shot us without asking us to leave or stop filming," Al Jazeera cited Mr Samoudi as saying. "The first bullet hit me and the second bullet hit Shireen.
"There was no Palestinian military resistance at all at the scene," he added.
Video of the shooting showed Abu Aqla was wearing a blue flak jacket clearly marked with the word "press", as well as a helmet.
A statement from Al Jazeera said: "In a blatant murder, violating international laws and norms, the Israeli Occupation Forces assassinated in cold blood Al Jazeera's correspondent in Palestine, Shireen Abu Aqla, targeting her with live fire early this morning... while conducting her journalistic duty."
The network called on the international community to hold the Israeli government and military accountable for the "intentional targeting and killing" of a journalist.
Qatar - which funds Al Jazeera - said it considered the killing a "heinous crime and a flagrant violation of international humanitarian law and a blatant infringement on freedom of media and expression".
Mr Abbas condemned the shooting of Abu Aqla and Samoudi and alleged that it was "part of the occupation's policy of targeting journalists to obscure the truth and commit crimes silently".
Mr Bennett accused Mr Abbas of making "baseless accusations".
"According to the information we have gathered, it appears likely that armed Palestinians - who were firing indiscriminately at the time - were responsible for the unfortunate death of the journalist," he said in a statement.
"Palestinians in Jenin were even filmed boasting: 'We hit a soldier; he's lying on the ground.' However, no [Israeli] soldier was injured, which increases the possibility that Palestinian terrorists were the ones who shot the journalist."
Israel's foreign ministry and the Israeli military tweeted a video showing a Palestinian gunman firing down an alleyway in the Jenin camp.
However, Israeli human rights group B'Tselem later said its researchers in Jenin had concluded that the Palestinian gunfire seen in that video could not possibly have been the gunfire that hit Abu Aqla and Samoudi.
In response, the Israeli foreign ministry stressed that "there was no claim that the gunfire in the clip killed" Abu Aqla.
Israeli military chief Lt Gen Aviv Kohavi meanwhile issued a statement saying: "At this stage, it is not possible to determine whose shooting she was hit by and we are sorry for her death."
Mr Bennett also said Israel had called on the Palestinian Authority to conduct a joint post mortem and investigation in order to get to the truth. He claimed that Palestinian officials had so far refused the offer, but a Palestinian minister said there had been no contact from Israel about a joint probe.
Abu Aqla joined Al Jazeera in 1997 and was one of its first field correspondents. She was one of the best known women to become a regular face on TV screens covering the Israeli-Palestinian conflict over the years.
Her colleague Nida Ibrahim said she was "very well respected" and that the news was "a shock to the journalists who have been working with her".
The Palestinian ambassador to the UK, Husam Zomlot, told the BBC's Newsday programme that she was a very close friend.
"She was a household [name] in Palestine, in the region and worldwide for being who she was - a prominent journalist who spent her life covering news, covering Israeli brutality in Palestine," he said.
The Israeli military frequently launches arrest raids into Jenin refugee camp. They have stepped up recently following a wave of attacks by Israeli Arabs and Palestinians on the streets of Israel and the West Bank in recent weeks that has left 17 Israelis and two Ukrainians dead.
At least 26 Palestinians have been killed - including assailants shot dead while carrying out attacks, or militants and civilians killed during Israeli raids and confrontations in the West Bank.
Israeli operations have centred on the Jenin district, where four of the Palestinians who carried out attacks in Israel came from.