“They’re all gone.”

For millions of people who recall the 1972 Olympics in Munich and who still shudder at the memory of the slaughter unleashed by terrorists there, those words are indelible. They were spoken by ABC’s Jim Mckay — the man behind the famous “thrill of victory, agony of defeat” introduction to the network’s long-running show, Wide World of Sports — when he learned that Israeli athletes and coaches taken hostage by terrorists from the Palestinian group Black September had been murdered.

McKay, a sportscaster who assumed the duties of a news anchor as one of the most shocking events of the 1970s unfolded on live TV, acquitted himself with unforgettable grace and intelligence as the story grew more abominable with each passing hour.

In fact, the simple, unadorned way that McKay reported the news that the Israeli hostages had, in fact, been killed still resonates today, four decades after the event:

“When I was a kid,” McKay began, in a strangely, comfortingly conversational tone, when he got word of what had happened, “my father used to say, ‘Our greatest hopes and our worst fears are seldom realized.’ Our worst fears have been realized tonight. They have now said there were eleven hostages; two were killed in their rooms yesterday morning, nine were killed at the airport tonight. They’re all gone.” [See the footage of the announcement here.]

There were hundreds of journalists from all over the world covering the 1972 Olympics, so the Black September assault and the murder of the Israeli athletes was, in fact, the very first time that a terror attack was reported and broadcast, in real time, across the globe. Among those journalists was LIFE magazine’s Co Rentmeester, a 36-year-old Dutch-born photographer who had distinguished himself (and been wounded by a sniper) while covering the war in Vietnam, and whose photography at the ’72 Olympics resulted not only in the chilling images presented in this gallery, but also in some of the most memorable sports pictures made at those Games.

Here, on the 40th anniversary of the September morning when the terrorists first attacked members of the Israeli team in their apartments in the Olympic Village and took them hostage, LIFE.com presents Rentmeester photos that ran in LIFE a few weeks after the murders — including one image (the first in this gallery) that for countless people became the photograph from the Munich Massacre: a portrait of, in the magazine’s phrase, “a masked figure of doom.”

In the end, 17 people died during the Black September attack: six Israeli coaches, five Israeli athletes, five of the eight terrorists and one West German policeman. Three terrorists were captured, but were later released by the West Germans. According to multiple reports (most of them denied by Israel) Israeli security agents later tracked down and assassinated many of those believed to be responsible for the Munich attack.

More recently, the Munich Massacre was again in the news when officials of the London Olympics decided against a 40th anniversary moment of silence during the 2012 opening ceremonies to honor those murdered in 1972. A moment of silence was observed, however, in the Olympic Village in July, during the traditional signing of the Olympic Truce — a surprise tribute by IOC president Jacques Rogge in the midst of an otherwise rote and predictable speech about ideals of fair play and fellowship at the Olympic Games.