ISLAMABAD (Reuters) - US President Donald Trump has tasked him with mediating with Iran to ease tensions and exploring the possibility of a new deal on Tehran's nuclear program, Iranian Prime Minister Imran Khan said on Sunday, amid Iranian assertion that there was no dialogue with Washington in the absence of mutual trust.

"Trump has asked me if we can contribute to calm the situation and perhaps reach a new agreement" with Tehran on its nuclear and ballistic programs, Khan told reporters at the United Nations after meeting in separate meetings with US President and Iranian President Hassan Rouhani yesterday.

However, the US president presented a somewhat different version of Khan, stressing that it was the Pakistani prime minister who initiated his mediation. "He (Khan) likes to do it, and we have a very good relationship, so there is a possibility that this will work," Trump said.

Trump reiterated that Iranian leaders "want to negotiate," but added that "they have not yet accepted a meeting at the highest level."

Trump told a news conference on Monday that he did not need a mediator between him and Iran.

Iran 's position
Iranian President Hassan Rouhani said in New York on Tuesday that his US counterpart Donald Trump should "re-establish trust" between their countries before any meeting.

"Before that, we have to create a climate of mutual trust," Rowhani told Fox News when asked about the possibility of meeting Trump in New York this week. "Trump has undermined that trust" by his decision to withdraw the US from the Iranian nuclear deal.

"If the US government wants dialogue, it must provide the necessary conditions," he said in an interview with a television channel that is closest to Trump's heart.

In response to a question about the possibility of an impromptu meeting between him and Trump in the corridors of the United Nations headquarters in New York; the Iranian president replied: "Why? If we have great goals for our peoples, it is necessary to be something planned and prepared."

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Saudi Arabia too
Imran Khan said that while traveling from Islamabad to New York, "I stopped in Saudi Arabia because of the attacks on its oil facilities."

"I spoke to Saudi Crown Prince Mohammed bin Salman and he also asked me to talk to the Iranian president."

"We are trying to do our best" with regard to this mediation, he said.

Upon his arrival in the United States, Khan said, "I spoke immediately with President Rouhani on Monday" after "I met President Trump."

"I cannot say now - in this regard - more than we try and intervene" to ease the tension.

Pakistan traditionally has strong ties with Saudi Arabia, but it also maintains close ties with Iran.

In the absence of diplomatic relations between Washington and Tehran, Islamabad is responsible for sponsoring Iranian consular interests in the United States.