President Moon Jae-in and U.S. counterpart Donald Trump also agreed to hold a meeting as early as possible to discuss North Korea and other pending issues.
In a message on Saturday, Rouhani expressed hope that Tehran and Seoul would witness further expansion of relations during Moon's tenure.
The talks involve both South and North Korea, Russia, the United States, Japan and China.
Only a few middle and high schools in South Korea have said that they would pick the books the state has issued.
Earlier this week, he said: "I will urgently try to solve the security crisis".
Park's father is slain military strongman Park Chung-hee, who ruled South Korea in the 1960s and '70s, and whose legacy as a successful economic strategist is marred by a record of vicious civilian oppression.
Mr Moon told Mr Abe to "look straight at history" and not make the past "a barrier".
The North's KCNA state news agency last week accused the US Central Intelligence Agency and South Korea's National Intelligence Service (NIS) of a plot to assassinate its "supreme leadership" with a biochemical weapon.
While South Korea, China and Japan all share worry about North Korea, ties between South Korea and China have been strained by South Korea's decision to install a USA anti-missile system in defence against the North.
China says the Terminal High Altitude Area Defence (Thaad) undermines its security, as its powerful radar can probe deep into its territory.
In a 40-minute conversation with Chinese leader Xi Jinping, the two agreed denuclearising Pyongyang was a "common goal" between them, Moon's office said.
At the invitation of China, a delegation led by Rep. Park Byeong-seug of the Democratic Party will attend the Belt and Road Forum for International Cooperation that will kick off on Sunday for a two-day run, senior presidential secretary for press Yoon Young-chan said in a briefing.
The US is the South's security guarantor and has 28,500 troops stationed in the country, but Seoul was startled when Trump suggested it should pay for the $1 billion THAAD system.
For his part, Moon said South Korea attaches great importance to its relations with China, and is willing to work with the Chinese side to develop bilateral ties and push forward their strategic cooperative partnership.
On Thursday, Moon asked Xi to help end the Chinese boycott of South Korean goods.
Beijing's displeasure over THAAD has reportedly been felt by South Korean businesses, particularly Lotte, the South Korean conglomerate that signed off on a land swap deal with the government to provide a site for the THAAD launch systems in late February.