He met Vijayan at the latter's official residence 'Cliff House' here. Haasan was treated to a feast arranged as part of the Onam festival celebrations.
On being quizzed about the Tamil Nadu politics, the actor said the governor should intervene in the present situation.
"I do not like to see this drama (going in Tamil Nadu). I am not anyone to call for a floor test or speak to the governor, but I am using this podium to call for it," he said.
Haasan said he had come to Kerala for a personal visit.
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"Most of the leftist are my heroes. I want to be in the middle of things and not take sides," he said.
"Look at the statistics of Kerala, you are pushing it to the standards of western countries. Mine is not blind admiration, it is sensible - about why choosing Pinarayi Vijayan," he remarked.
Talking about the meeting on his Facebook post, Vijayan said he shared a healthy friendship with the actor.
Though it was a courtesy meeting, politics of south India, especially the situation in Tamil Nadu, also came up for discussion, he added.
Talking to reporters before leaving to meet the Kerala chief minister, the Tamil actor said his visit was "a political education tour."
"Definitely, as far as I am concerned, this is an education tour to me," he said.
"Actually I was supposed to come to Kerala last year itself. But I could not make it as I met with an accident," Haasan said.
Haasan had been vocal against the Tamil Nadu government on the issue of corruption, thus incurring the wrath of several state ministers, who have accused the actor of speaking in general terms and dared him to provide evidence of his charges.