Mr. Najib appeared eager to bring some finality to the families of the passengers, who had complained for more than two weeks about the incomplete and sometimes contradictory information they were getting. Two-thirds of the plane’s passengers were Chinese citizens, and the flight was bound for Beijing when it took off from Kuala Lumpur, Malaysia, after midnight on March 8.

But many furious Chinese relatives and friends of passengers refused to believe it, wailing with anguish and screaming that the Malaysians were lying and hiding what they knew.

“The Malaysian government is not telling the truth,” said one woman among the relatives of passengers who gathered at the Lido Hotel in Beijing to wait for news of the flight. “All governments are corrupt. The Malaysian government is hiding something.”

The announcement did little to solve the deeper mystery of the plane’s disappearance, shedding no light on why someone with detailed knowledge of the plane’s navigation and flight systems diverted it radically from its course. Investigators said they have looked into the backgrounds of the 239 people on board, including the two pilots and the crew, and have so far found no answers to that central question.

Image Relatives of passengers of the Malaysia Airlines flight missing since March 8 reacted to a news broadcast from Malaysia in a Beijing hotel on Monday. Credit... Rolex Dela Pena/European Pressphoto Agency

However long expected, the news that the jet was lost came as a body blow, dashing the hopes that many had clung to with increasing desperation that somehow the plane had been hijacked and taken to some obscure spot where the passengers could still be alive.

A few people in the hotel ballroom in Beijing collapsed and were put on wheeled stretchers and taken to the parking lot, which was full of police cars and ambulances. Inside the hotel, police officers in navy-blue uniforms stood guard every few feet and blocked scores of jostling journalists from entering the ballroom. Several women emerged sobbing so hard that knots of friends and family had to help them walk to the elevators.

“We demand the truth,” said a young woman in a red ski jacket. “The Chinese government should step up and find out the truth for us. Nobody cares about us. Nobody cares about the lives of our family.”

Li Chengpeng, a popular Chinese social critic, gave voice to the deep skepticism held by many Chinese of the official announcement. He posted a message for the seven million followers of his microblog, calling Mr. Najib’s news conference staged theater. “Just now, they were not actually publicizing the truth but were merely giving a show of publicizing the truth,” he wrote. “It looks like there are traces of rehearsal. Politicians are shameless! Keep investigating!”