BEIJING — The widow of Liu Xiaobo, the Chinese winner of the Nobel Peace Prize who died of cancer while under police guard last month, has resurfaced for the first time since his death in a brief online video pleading for privacy and time to recover from her grief.

But many supporters of Liu Xia, Mr. Liu’s widow, said the video of just over one minute appeared to have been made by Chinese security authorities who have kept Ms. Liu under secretive guard, cut off from family and friends.

In the video, which appeared on YouTube on Friday, Ms. Liu said in a weak, rasping, halting voice that she was away from Beijing and still recovering from the death of her husband, who was 61. Mr. Liu’s liver cancer was disclosed only after it was too late for real hope of a cure.