AP's President and CEO Gary Pruitt said the agency was "shocked and horrified" at the strike. Meanwhile, Al Jazeera said they “would not be silenced”.
The companies’ staffers and other tenants safely evacuated the building after the military telephoned a warning that the strike was imminent within an hour. Three heavy missiles struck the building, collapsing it in a giant cloud of dust.
"The world will know less about what is happening in Gaza because of what happened today," Mr Pruitt said in a statement.
"We are shocked and horrified that the Israeli military would target and destroy the building housing AP's bureau and other news organisations in Gaza.
"This is an incredibly disturbing development. We narrowly avoided a terrible loss of life.”
He added that the AP was seeking information from the Israeli government and was engaged with the U.S. State Department to learn more.
The building also housed residential apartments.
The Israeli military said it targeted the building because it contained assets of Hamas intelligence agencies, which it said were using media offices as "human shields." It did not provide evidence for the claims.
Hours earlier, another Israeli air raid on a densely populated refugee camp killed at least 10 Palestinians from an extended family, mostly children, the deadliest single strike of the current conflict.
The New York-based Committee to Protect Journalists demanded Israel "provide a detailed and documented justification" for the strike.
"This latest attack on a building long known by Israel to house international media raises the spectre that the Israel Defense Forces is deliberately targeting media facilities in order to disrupt coverage of the human suffering in Gaza," the group's executive director, Joel Simon, said in a statement.
The strike on the building housing media offices came in the afternoon, after the owner received a call from the Israeli military warning that the building would be hit within the hour.
A video broadcast by Al-Jazeera showed the building's owner, Jawwad Mahdi, pleading over the phone with an Israeli intelligence officer to wait 10 minutes to allow journalists to go inside the building to retrieve valuable equipment before it is bombed.
"All I'm asking is to let four people ... to go inside and get their cameras," he says.
"We respect your wishes, we will not do it if you don't allow it, but give us 10 minutes." When the officer rejected the request, Mahdi said, "You have destroyed our life's work, memories, life. I will hang up, do what you want. There is a God."
Al-Jazeera, the news network funded by Qatar's government, broadcast the airstrikes live as the building collapsed.
"This channel will not be silenced. Al-Jazeera will not be silenced," Halla Mohieddeen. on-air anchorperson for Al-Jazeera English said, her voice thick with emotion. "We can guarantee you that right now."
Later in the day, the White House responded by saying Israel had a "paramount responsibility" to ensure the safety of journalists covering the spiralling conflict. US President Joe Biden has urged a deescalation in the 5-day conflict between Hamas and Israel, but has publicly backed Israel's right to self-defence from Hamas rockets fired from Gaza.
White House press secretary Jen Psaki tweeted Saturday that the U.S. had "communicated directly to the Israelis that ensuring the safety and security of journalists and independent media is a paramount responsibility."
The attack was also criticised by the UK’s shadow foreign secretary Lisa Nandy, who said that “press freedom is a fundamental right”.
Since Monday night, Hamas has fired hundreds of rockets into Israel, which has pounded the Gaza Strip with strikes.
In Gaza, at least 139 people have been killed, including 39 children and 22 women; in Israel, eight people have been killed, including a man killed by a rocket that hit in Ramat Gan, a suburb of Tel Aviv, on Saturday.