His remarks follow months of speculation about the health of Ayatollah Mojtaba Khamenei, who has not been seen in public since an air strike that killed his father and predecessor, Ali Khamenei, at the start of the Iran war.
"The interaction level with our dear Supreme Leader is increasing day by day and should increase so that we can solve our problems with his guidance," Pezeshkian said in the clip.
Mojtaba Khamenei suffered severe facial and leg injuries in the February 28 attack, three people close to his inner circle told Reuters in April.
Khamenei has issued written statements since his appointment as Iran's third supreme leader by a clerical body on March 8 but no new image or voice recording has accompanied them.
Senior sources told Reuters in July that the lack of an image or a voice recording was due to health and security considerations.
The security risks are substantial given the assassination of his father in the first US and Israeli strikes, which were launched during diplomatic efforts to resolve disputes between the countries.
Mojtaba Khamenei owes his elevation to Iran's Revolutionary Guards, who backed him as a reliable guardian of their hardline agenda.
Already strengthened by war, the Guards' growing dominance signals a more aggressive foreign policy and tighter domestic repression, sources familiar with the country's inner policy-making circles told Reuters in April.