"Karroubi won't withdraw because he has made a lot of effort to maintain his position," said Abolfazl Shakoori with the National Confidence Party.
Karroubi launched the NCP following a failed presidential bid in 2005. He is a former member of the Association of Combatant Clerics and former speaker of the Iranian Parliament.
Shakoori made his comments following a meeting between Karroubi and former President Mohammad Khatami, Iran's Press TV reports. Khatami withdrew from the race in March, citing a need for party unity in the Reformist slate.
Some officials in the Reformist camp have called for Karroubi to step aside in favor of former Iranian Prime Minister Mir-Hossein Mousavi, who received sweeping support from several Reformist parties during the weekend.
Reformists have predicted that growing frustration with the current Iranian leadership would bring the ticket a resounding victory in the June presidential elections.
The Principlist camp has so far not announced its candidate for president, though incumbent President Mahmoud Ahmadinejad is widely expected to seek another term on that ticket.
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