Riyadh, Washington asked Pakistan to mediate amid Iran tensions
Khan met both US President Donald Trump and Iranian President Hassan Rouhani at the United Nations, before which he visited Crown Prince Mohammed bin Salman in Saudi Arabia.
"Trump asked me that if we could de-escalate the situation and maybe come up with another deal," Khan told reporters.
"Yes, we did convey this, and yes, we're trying our best," he said.
"I immediately spoke to President Rouhani yesterday after the meeting with President Trump. I can't say anything right now more than this except that we're trying and mediating," he said.
In Saudi Arabia, which was hit earlier this month by attacks on its oil infrastructure blamed on Iran, Crown Prince Mohammed "also asked me to talk to the Iranian president," Khan said.
Pakistan traditionally has strong relations with Saudi Arabia but also maintains ties with Iran, with Islamabad representing Tehran's consular interests in the United States in the absence of diplomatic relations.
But despite Trump's request, the US president did not hold back at the UN General Assembly on Tuesday.
Trump warned sanctions on Iran would be increased unless it ceases its "fanatical" weapons drive and "aggression" in the Middle East.
"Hoping to free itself from sanctions, the regime has escalated its violent and unprovoked aggression," Trump told the United Nations during its 74th General Assembly in New York.
Trump also criticised Tehran's "menacing behaviour" when addressing the 193 member states of the UN.
He encouraged all nations to combat Tehran's influence, saying "no responsible government should subsidise Iran's bloodlust".
The president showed no signs of loosening sanctions on the Islamic Republic.
"Hoping to free itself from sanctions, the regime has escalated its violent and unprovoked aggression," Trump told the United Nations General Assembly in New York.
"As long as Iran's menacing behaviour continues, sanctions will not be lifted - they will be tightened."
Trump accused Iran of "anti-Semitic behaviour" for its criticism of Israel and called on the loyalty of other nations in the region to battle "extremism".
Meanwhile, the leaders of France, Germany and Japan were all also meeting with both Rouhani and Trump at the United Nations in hopes of reviving diplomacy.
Follow us on Twitter: @The_NewArab