He has said he would be prepared to go to Pyongyang "if the conditions are right".
Mr Moon's office said the new president also spoke with Vladimir Putin on Friday - with the Russian leader pledging to play a constructive role in resolving the North Korea crisis.
"A Korean-style, anti-terrorist offensive will be commenced to mop up the intelligence and plot-breeding organisations of the US and South Korea", mission said in a statement.
China bitterly opposes the deployment of the system, which it says will upset the strategic balance in the region, and during the campaign Mr Moon said he would review the system once he was elected.
The Trump administration has unfolded a strategy of maximum pressure and engagement toward North Korea and has especially focused on bolstering sanctions on the Kim Jong-un regime.
Regional experts have believed for months that North Korea is preparing for its sixth nuclear test.
In a message on Saturday, Rouhani expressed hope that Tehran and Seoul would witness further expansion of relations during Moon's tenure.
On Thursday, the US director of National Intelligence, Dan Coats, told the Senate Intelligence Committee that North Korea posed "a very significant, potentially existential threat to the United States that has to be addressed". North Korea is severely isolated from the global community at the moment.
North Korea, which considers China its sole major diplomatic ally and economic benefactor, is also expected to send a delegation to the two-day meeting in Beijing, the Chinese foreign ministry has said.More news: Monaco won't celebrate title yet - Jardim
Trump has called on Beijing to do more to rein in North Korea, while China is angry over THAAD, which it be-lieves could pose a threat to its military.
If Moon is willing to open up relations with North Korea again, another question is to what extend?
Via various media, the communist state called on the new South Korean government to change the previous government's North Korea policies. There is also the question of the US' recent deployment of the THAAD anti-missile defence system in South Korea. North Korea continued its progress in becoming a nuclear state.
Mr Moon told Mr Abe to "look straight at history" and not make the past "a barrier".
Yoon said the dispatches were mentioned during the first telephone conversation between Moon and Chinese President Xi Jinping which lasted for 40 minutes beginning at about noon.
"I am well aware of the concern and fear of the Chinese about the THAAD deployment", Moon was quoted as saying when Xi explained the Chinese stance on the matter.
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.
Beijing has branded THAAD and its powerful radar as a threat to its security and has retaliated against some South Korean firms.