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Khan told Al Jazeera that talks between the two regional rivals are ongoing, at a slow pace, but that Islamabad's efforts prevented an escalation between the two sides.
"Our mediation between Iran and Saudi Arabia has not stopped and we are making progress but slowly," Khan told Al Jazeera in an exclusive interview with the broadcaster.
"We have done our best to avoid a military confrontation between Iran and Saudi Arabia, and our efforts have succeeded."
Iran and Saudi Arabia have been at loggerheads for decades, but tensions escalated following accusations by Riyadh that Tehran is supplying ballistic missiles to Houthi rebels in Yemen, which have been fired into the kingdom.
Missile and drone strikes on Saudi Arabia's oil infrastructure have also been blamed on Iran.
Khan also accused India of coming under an "extremist ideology" under Prime Minister Narendra Modi with Muslims the target.