Prompted by Washington, former cricket great Khan in October visited Tehran and Riyadh to facilitate talks after attacks on Persian Gulf oil interests that the United States blamed on Iran, Reuters reported.
"Our mediation between Iran and Saudi Arabia has not stopped and we are making progress, but slowly," Khan told Al Jazeera in extracts the broadcaster released from an interview to be aired in full on Wednesday.
"We have done our best to avoid a military confrontation between Iran and Saudi Arabia, and our efforts have succeeded," Qatar-based Al Jazeera also reported Khan as saying.
Last October, Imran Khan visited Iran as part of a Pakistani initiative to defuse tensions in the Persian Gulf and mediate between Iran and Saudi Arabia.
At a joint press conference with Iranian President Hassan Rouhani in Tehran, he said Islamabad will do its utmost to enable talks between Iran and Saudi Arabia.
"Pakistan does not want conflict between Iran and Saudi Arabia...I am happy to facilitate talks between Tehran and Riyadh...I am very hopeful as I had constructive talks with the (Iranian) president," he said.
Iran has always said that it is ready to hold talks with Saudi Arabia, with or without mediation.
Prior to Khan’s visit to Tehran, Iran's foreign minister said Tehran welcomes efforts by intermediaries to arrange talks with Saudi Arabia.
"We've always been open to discussing anything with Saudi Arabia. Saudi Arabia is our neighbor. We're going to be here together permanently," Mohammad Javad Zarif said, according to Press TV.
"We don't have any choice but to talk to each other, and we have been open to talking to Saudi Arabia either directly or through intermediaries," Zarif noted.
"We've never rejected any intermediary... We've always been open to mediation, and we've always been open to direct talks with our Saudi neighbors," the top diplomat noted.
Relations between Tehran and Riyadh began to seriously strain in 2015, when Saudi mismanagement of the annual Hajj pilgrimage led to a stampede that killed about 4,700 people, including more than 460 Iranians.
Saudi Arabia cut its ties with Iran in early 2016 following angry protests in front of its diplomatic missions in the capital Tehran and the holy city of Mashhad against the kingdom's execution of senior Shia cleric Sheikh Nimr al-Nimr.
The frictions between Tehran and Riyadh worsened following a September 14 attack on Saudi oil facilities.
The United States and Saudi Arabia rushed to blame Iran for the assault on the facilities, a claim Tehran denied. Then, an Iranian-flagged oil tanker was damaged by two separate explosions off the Saudi port of Jeddah, raising fears of a further escalation.
In recent years, Saudi Arabia has also supported the US maximum pressure on Iran following Washington’s unilateral withdrawal from the 2015 nuclear agreement.