Pezeshkian replaced the ultraconservative Ebrahim Raisi, who died in a helicopter crash in May.
During election campaigning, he had vowed to "fully" oppose police patrols enforcing the mandatory hijab headscarf, as well as easing long-standing internet restrictions.
Relations with the West
At his news conference, Pezeshkian briefly touched on other topics including Iran's fraught relations with the United States and the 2015 nuclear deal.
"We do not want to fight with America if it respects our rights," he said. "It is not us who are hostile (to the Americans). We have not built military bases around their country," Pezeshkian added, referring to U.S. bases in the Gulf and in Iraq.
Iran and the United States have had no diplomatic relations since 1980, the year after the Islamic Revolution that toppled its Western-backed Shah Mohammed Reza Pahlavi.
'Disarm Israel'
He also insisted on Iran's right to maintain its missile program, which has drawn Western criticism, as a deterrent against its arch-foe Israel.
"They (the West) want us not to have missiles, that is fine, but you need to disarm Israel first," he said, adding that otherwise "they can drop bombs on us whenever they want, like in Gaza."
US presidents are highly constrained in how they can use their power. Why would you expect Iranian presidents to be any different? They have even less power on paper because Iran also has a Supreme Leader.