Davidson, 25, introduced musical guests Miley Cyrus and Mark Ronson, who were joined in a surprise performance by Sean Ono Lennon for John Lennon's song "Happy Xmas (War Is Over)." Davidson's quick intro may have been just enough to ease fans' worries
Davidson also appeared as "Bohemian Rhapsody" star Rami Malek in a sketch about possible Oscar hosts, but that was pre-taped.
Davidson, who suffers from borderline personality disorder, which he has referred to in the program, posted a screenshot of a note Saturday saying that he did not "want to be on this earth anymore" and was not sure "how much longer" he could be.
Lt. Paul Ng of the New York Police Department told USA Today on Saturday that police did a "wellness check and made contact" with Davidson following his post. He was reportedly working on the set of "Saturday Night Live" at 30 Rock in Manhattan.
Davidson's note was preceded by a "bravo" to Kanye West, who had just discussed his struggle with bipolar illness.
"I can't explain to you enough how difficult and scary it is to be honest about stuff like this," Davidson wrote. "We need people like Kanye."
Davidson, who recently broke up with singer Ariana Grande, posted a message earlier this month saying that he would not kill himself "no matter how hard the internet or anyone tries to make me."
CORRECTION: An earlier version of this story called the Lennon song "And So This Is Christmas." The title is "Happy Xmas (War Is Over)."