During his day-long visit to Tehran on Sunday, Khan said that a war between Iran and Saudi Arabia should never happen, Geo News reported.
"The issue is complex but can be resolved through dialogue. Pakistan does not want any conflict in the region," he said.
Khan emphasised that Pakistan did not want a conflict between Iran and Saudi Arabia while recognising that it was a complex and complicated issue.
"This visit to Iran and the visit that I will undertake to Saudi Arabia on Tuesday is a Pakistan-led initiative. I will go with a positive mind to Saudi Arabia and Pakistan will play the role of a facilitator," he said, stressing that he was willing to host both countries in Islamabad.
"When I was in New York, I was asked by US President Trump to facilitate these talks and we will do all what we can. We would facilitate so that sanctions can be lifted (and) a nuclear deal can be signed," Khan said.
In his address, the Iranian President said: "I told Prime Minster Imran we welcome any gesture by Pakistan for peace in the region and appreciate his visit to our country," Dawn news reported.
The President added that the two leaders had discussed, among other things, the war in Yemen and the US sanctions bon Iran.
"Regional issues have to be resolved through regional means and dialogue. We also emphasised that any goodwill gesture will be responded with a goodwill gesture and good words.
"We also discussed how the nuclear deal could be restored," added Rouhani.
Following the joint conference, Khan called on Supreme Leader of Iran Ayatollah Ali Khamenei, the Prime Minister's Office said in a statement.
The premier during his meeting with Khamenei "reaffirmed his resolve to comprehensively upgrade Pakistan-Iran relations".
"He also apprised the Supreme Leader of his initiative for regional peace and security," the statement added.
Khan also held a meeting with Iranian Foreign Minister Javad Zarif, who had received him upon his arrival.
This is Khan's second visit to Iran this year. In April, he undertook a two-day official trip on President Rouhani's invitation.
The mediation initiative is being taken at the request of Saudi Arabia. Crown Prince Mohammad bin Salman had during Khan's last visit to Saudi Arabia asked him to help defuse tensions with Iran as Riyadh wanted to avoid war.
Tensions have been brewing between Tehran and Riyadh since the September 14 drone attacks on a Saudi oil facility and a processing plant.
Although the Yemeni Houthi rebels have claimed responsibility, both Saudi Arabia and the US have blamed Iran for the drone strikes - a charge Tehran has strongly rebutted.
( With inputs from IANS )