File Photo: Turkish President Recep Tayyip Erdogan addresses a press conference at the end of the G20 of World Leaders Summit on October 31, 2021 at the convention center La Nuvola in the EUR district of Rome. AFP
In a statement, the police said they were investigating 30 people who used or retweeted the hashtag #olmus (#heisdead), which became a top trending topic on Turkish Twitter.
Underscoring the government's sensitivity about the posts, Erdogan's communications director Fahrettin Altun posted a short clip on Wednesday showing the Turkish leader walking out of his official car along a turquoise carpet.
"Trust to friends, fear to enemies," Altun wrote.
Rumours about the health of Erdogan, 67, have been swirling for years, with one of his doctors going on record in 2011 to deny that the Turkish leader had cancer.
Erdogan underwent laparoscopic gastrointestinal surgery that same year, and has been walking more gingerly ever since.
Erdogan met US President Joe Biden on the sidelines of the G20 summit in Rome on Sunday.
He then cancelled his planned attendance at the COP26 climate conference in Glasgow, citing a dispute over the security protocol.
The latest wave of speculation appears to have been prompted by Erdogan's failure to attend a ceremony of his ruling party, which on Wednesday celebrated the 19th anniversary of its rise to power.
The official Anadolu news agency later issued footage of Erdogan -- first standing, then seated in silence -- meeting in the capital Ankara with Baghdad Amreyev, who heads a council of Turkic-speaking central Asian states.
His office said Erdogan would also receive diplomatic credentials from a new group of ambassadors to Turkey.