"Since Mr Mesic has not apologised to date, nor has he shown any intention of doing so, Jadranka Kosor will not participate in duels on RTL Television, Nova TV, Radio 101 and Family Radio," her election team said in a statement on Monday.
The statement said that Kosor had accepted the duels "before a series of insults and insinuations unworthy of a president" came from the current president, and accused Mesic of "falsely presenting himself as a tolerant and democratic president".
The HDZ presidential candidate will participate in a confrontation of all presidential candidates on Croatian Television on December 30, her election team said.