Essebsi, 92, was taken to a military hospital after suffering what the presidency called a "severe health crisis".
His hospitalization and reports of his death only served to add to the insecurity in Tunisia, where lawmakers recently passed a law aimed at sidelining from running for office individuals who "distribute aid or resort to political advertising, from running for office".
Mr Chahed said in a Facebook post (in Arabic) that he had visited the president in hospital.
Shortly afterwards key adviser Firas Guefrech said on Twitter that the president was in "critical condition".
Essebsi was born in November 1926 and took over the Tunisian presidency after winning the 2014 presidential elections.
Tunisia set itself on a path to democracy without much of the violence seen elsewhere, although it has been the target of militant Islamists over the years.
Tunisia, whose 2011 revolt toppled longtime dictator Zine El Abidine Ben Ali and sparked the Arab Spring uprisings, has been hailed as a model of democratisation in the Arab world, but has faced economic woes and jihadi attacks.
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The Tunisian Ministry of Interior has closed the roads leading to the presidential palace following two suicide attacks targeted police personnel in the Avenue of Habib Bourguiba on Thursday.
Government troops have been battling militant groups in remote areas near the border with Algeria, while high unemployment has also stoked unrest in recent years.
He led the immediate transition as prime minister in 2011 and was elected president three years later. The party has not identified another candidate yet.
Presidential elections are due on November 17, after parliamentary elections which have been scheduled for 6 October.
Under a new constitution guaranteeing democratic freedoms, Essebsi has limited powers compared with Ben Ali.
FILE - In this photo taken on Oct.3, 2018 Tunisian President Beji Caid Essebsi is pictured during a joint press conference with his Djibouti counterpart at the presidential palace in Carthage, near the Tunisian capital, Tunis.