In 1992, Army of Lovers re-released the single exclusively for the United States and includes remixes only found in this version; it reached number 11 on the Billboard Dance Club Play chart.

Andy Kastanas from The Charlotte Observer complimented "Obsession" as "another good song that deserves a listen".

[1] Ian Gittins from Melody Maker commented, "I was sufficiently moved by the Abba-harmonies and high camp of Army of Lovers' "Crucified" to make it Single Of The Week, but this time the Swedish cartoon trio are far less instant.

[1] It entered the top 10 in Austria, Belgium, Finland, Germany, Greece, the Netherlands, Spain, Sweden and Switzerland.

In the United Kingdom, "Obsession" peaked at number 67 during its first week on the UK Singles Chart, on December 22, 1991.