Rouhani, who is seen by some as a moderate leader, led Iran from relative global isolation when he signed a nuclear deal in 2015 with several world powers in exchange for the lifting of sanctions against the country.
David Cohen, the former Central Intelligence Agency deputy director, said President Donald Trump's tasking a team whose goal is to justify a pullout from the Iran deal posed a "grave danger" to the USA ability to face global threats.
For his turn, Larijani reaffirmed "active support" for efforts to resolve the North Korea issue.
"We will certainly not fall into the trap of USA policy and Trump, and our reaction will be very carefully considered", he said.
Rouhani also urged further expansion of economic ties between the two countries, saying Iran welcomes South Korean companies seeking business opportunities in various fields including energy, chemical, and other high-tech industries in the country.
Tillerson says United States will respond to Russia's embassy expulsion move by September
Neither Tillerson nor Lavrov responded to a shouted question about how the new USA penalties might affect their discussions. Trump denies any collusion and has repeatedly questioned United States intelligence about Moscow's involvement.
"The U.S. lack of commitment to implementation of the nuclear deal ... proved it to be an unreliable partner to the world and even to its longtime allies", Rouhani said in the ceremony broadcast live on state television.
Senior members of the Palestinian terrorist group Hamas met with Iranian Foreign Minister Mohammad Javad Zarif in Tehran on Monday.
Ali Akbar Velayati, a senior adviser to Supreme Leader Ayatollah Ali Khamenei, also asked Europe to "take a more independent policy towards Iran" state media reported.
Rouhani's deputy said on Wednesday that Rouhani would keep on two important ministers for his second term: Oil Minister Bijan Zanganeh, who is largely credited with closing a deal with the French oil major Total, and Foreign Minister Zarif, Iran's lead negotiator in the nuclear agreement.
While he spoke much about women's rights during his campaign, Rouhani is not expected to select any women for his cabinet.