In all probability: this is a tobacco pipe bowl made from clay/ceramics. Probably it was glazed with some sort of faience when new. Made in Tunis workshops. The general style seems to be ubiquitous for Mediterranean clay pipes, especially form the Ottoman era. The 'Tunis' location is thus just a hint for localised production, but no guarantee.
The actual age is hard to ascertain from a photo alone. Below is one example picture with three of the numerous styles found for this basic appliance (more in the link given).
Qallaline potteries were in operation in Tunis from the late 16th century until the 1920s. The chibouk style tobacco pipe, called sebsi (p. sbesi) in Tunisia, is a bowl usually made of clay with separate stem and mouthpiece which was in use throughout the Mediterranean, becoming increasingly more common from the 17th to early 20th centuries.
— John Wood: "A study of clay tobacco pipes in Tunis. Were they traded to Gozo (Malta)?", Post-Medieval Archaeology, Vol 33, pp233–241, 1999. link
When on auction today, a nice collection of this type might look like this:
— Ensemble De Trois Fourneaux De Pipe Et Une Pipe En " Tophané " en terre cuite vernissée, ciselée et sculptée. (Usures et décoloration des fourneaux. La pipe est complète) Turquie, Tophané, fin du 19e siècle. Long. de la pipe : 23 cm Long. des fourneaux : 7 cm env.
Note that "Qallaline" in the first quote denotes a type of glazed ceramics from Tunis, named so after a street in the city, therefore that's a toponym turned object-style-identifier, just like the word china is used for porcelain.
— Alain Loviconi & Dalila Loviconi: "Les faïences de Tunisie: Qallaline & Nabeul", Institut du monde arabe (France) Edisud: Aix-en-Provence, Tunis, 1994.
An even closer visual match overall might be:
[…] These concerns are addressed particularly well by finds of utilitarian items such as a small assemblage of 21 clay pipes and three other smoking-related artifacts recently excavated from the ca. 1765 Sadana Island ship which sank at anchor while loaded with coffee, porcelain, qulal, and other goods. Analysis of the assemblage specifically contributes to questions of chronology and typology and presents new evidence for regionalism, style, and the impact of far-reaching trade routes on markets with a global perspective.
b) S21 (MH 5.1 cm) illustrate cylindrical and flared chimney types respectively. […] S21 has a dark brown, burnished slip (Drawings Lara Piercy).
[…] The fixed date for the shipwreck is a major contribution for clay tobacco pipes studies of the Ottoman Empire. […]
— Cheryl Ward & Uzi Baram: "Global Markets, Local Practice: Ottoman-period Clay Pipes and Smoking Paraphernalia from the Red Sea Shipwreck at Sadana Island, Egypt", International Journal of Historical Archaeology, Vol. 10, No. 2, June 2006 DOI: 10.1007/s10761-006-0006-2
Aspects that may be speaking against this identification theory:
- We have not seen all sides of the object in question. If the small end is not hollow, then this answer is moot.
- If accurate, the measurements provided would indicate a rather large and massive bowl. Thus the weight of the object's remains might be interesting as well. This is still quite possible for regular pipes, but as far as I know not that common over all for early tobacco pipes, and it may thus indicate a rather younger date — if it is a pipe for tobacco.
A match for the shipwreck bowl indicates that the size was quite common for a time.
Both objections seem rather insignificant so far.