[1] He was a candidate in the presidential election held on 3 April 2004, and although pre-election polls had suggested he would come first, he actually came in third behind the eventual President Ivan Gašparovič and former prime minister Vladimír Mečiar, thus preventing him from contesting the run-off.

In 1999, Kukan was appointed United Nations Special Envoy on Kosovo by UN Secretary General Kofi Annan, a role he held alongside Carl Bildt.

[2] Kukan graduated from The Moscow State Institute of International Relations in 1964, where he also gained a strong knowledge of the Swahili language.

In the election campaign, he led the list of candidates of the centre-right Slovak Democratic and Christian Union (SDKÚ).

In 2010, Kukan joined the Friends of the EEAS, an unofficial and independent pressure group formed because of concerns that the High Representative of the Union for Foreign Affairs and Security Policy Catherine Ashton was not paying sufficient attention to the Parliament and was sharing too little information on the formation of the European External Action Service.