The Islamic State group claimed responsability for the double suicide attacks in Tunisia's capital, Tunis on Thursday, according to US-based monitor SITE Intelligence Group. Meanwhile, President Essebsi was hospitalised after being taken ill soon after the attacks.
Presidential advisor, Firas Guefrech said 92-year-old Beji Caid Essebsi was "critical" then "stable".
Essebsi is the country's first democratically elected president. He came to power in 2014.
Since then, five terror attacks have been carried out in Tunisia, in the capital, targetting military or police, or in tourist locations.
The most recent before Thursday's double attack was on 29 October 2018, near police cars on Habib Bourguiba Avenue, also a sucide attack.
Tourism Minister Rene Trabelsi said tourism sites remained open. Tourism accounts for 14 per cent of Tunisia's revenues.
The attacks come as presidential and legislative elections are scheduled for October and November in Tunisia.Essebsi has said he will not stand for re-election.
French President Emmanuel Macron strongly condemned the bombing in central Tunis on Thursday. He sent a tweet from Japan where he is attending the G20 meeting saying, "I firmly condemn these attacks which struck in the heart of Tunis today," and France stands alongside the Tunisian people at this difficult moment."