In the video, taken at a cafe in Jerusalem's outskirts and posted on Netanyahu's Telegram and X accounts, his aide asks him about the rumours.
Netanyahu responds with a pun on the word dead - which in Hebrew slang can be used to describe "being crazy about" someone or something - as he reaches for a cup of coffee.
"I'm crazy about coffee. You know what? I'm crazy about my people," Netanyahu tells the aide.
Reuters verified the video's location from file imagery of the cafe, which matched the interiors seen in the video.
The date was verified from multiple videos and photos of Netanyahu's visit posted by the cafe on Sunday.
Since the US and Israel launched attacks on Iran on February 28, Netanyahu has visited at least two towns hit by Iranian missiles, a hospital, port and military bases but there was little to no media access, and videos were distributed by his office.
Netanyahu, who rarely gives interviews to Israeli press or holds news conferences, convened his first press conference since the start of the war via a video link on Thursday, a similar format to the one he used in June during Israel's 12-day war with Iran.
Emergency safety restrictions in Israel since the start of the war ban public gatherings and have kept most people at home or close to shelters and safe rooms, with schools shut across most of the country.
