An kafa majalisa ta zamani, Alþingi (Ingilishi: Althing), a 1845 a matsayin mai ba da shawara ga masarautar Denmark. An yi la'akari da shi a matsayin sake kafa majalisa da aka kafa a 930 a zamanin Commonwealth kuma duk da haka an dakatar da shi na ɗan lokaci daga 1799 zuwa 1845. Saboda haka, "za a iya cewa shi ne mafi tsufa a duniya". A halin yanzu yana da mambobi 63, wanda aka zaɓa don tsawon shekaru hudu. Shugaban gwamnati shi ne firaministan wanda, tare da majalisar, ke da alhakin gwamnatin zartarwa. Tambaya: Iceland ta dakatar da gwamnatin majalisa na ɗan lokaci daga wane kwanan wata?
1799 zuwa 1845