The comments reported on opposition websites on Monday were the first such recognition from Karoubi, who came fourth in June's disputed presidential election and who has persisted in challenging the government over the result.
The vote was followed by huge opposition protests and plunged Iran into its deepest internal turmoil since the 1979 Islamic revolution, exposing divisions in the establishment.
"I will continue to the end of the road on the side of the nation and will do my best to see free election held and eliminate existing obstacles," Sahamnews cited Karoubi as saying on Tuesday.
Sahamnews is the website of Karoubi's political party, Etemad-e Melli. Karoubi is a pro-reform cleric and fierce critic of the hardline president.
"I will soon inform the people of my detailed position on the revolution's ideals, defence of the public's rights and the necessity of holdig free elections," Karoubi said.
"One of the biggest rights of this nation is the votes that were cast in the ballot boxes."
The reformist opposition says the poll was rigged to secure Ahmadinejad's re-election. The authorities deny the charge of vote fraud.
Karoubi was also cited as saying this week that he did not believe that Ahmadinejad -- whose first term saw tension with Washington over Iran's nuclear energy programme -- would complete his four-year term.
A major oil producer, Iran is locked in dispute with Western powers who fear the nuclear programme is aimed at acquiring nuclear weapons. Iran, which could face more United Nations sanctions, says it is only interested in generating electricity.