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The two leaders "had a productive conversation about how the US and Pakistan will have a strong working relationship in the future", the transition team said in a statement.
Trump told Sharif in a telephonic conversation that "he is looking forward to a lasting and strong personal relationship" with him, it added.
Although Indian Prime Minister Narendra Modi and Trump had spoken when Modi called him to congratulate him on his victory soon after the election results were announced, the conversation with Sharif was the first with a South Asian leader after the beginning of the transition process.
The tenor of Trump's outreach to Pakistan might surprise some who had expected him to take a strong line against Islamabad because of his criticism of that country and vehement opposition to Islamist terrorism during the campaign.
But the friendlier tone he has taken was in keeping with other assertions he made acknowledging the special risks Pakistan posed with its nuclear weapons and its "semi-stable state".
Because of that, he said in a TV interview during the campaign: "We have a little bit of a good relationship.
I think I'd try and keep it."
Pakistani media reports said that during the conversation with Sharif, Trump had offered to play any role he could to help Islamabad find solutions to its problems.
Trump also told Sharif that he looked forward to visiting Pakistan and meeting him, according to Samaa News.
Last month, in an interview to The Hindustan Times, Trump had called the situation between India and Pakistan "very, very hot tinderbox" and offered to "mediate or arbitrate", if asked to.
India opposes any third party involvement in its bilateral disputes with Pakistan.
During his campaign, Trump criticised Pakistan for allowing some terrorist groups to operate from its soil.
He ridiculed President Barack Obama's administration for not being able to help the jailed doctor who helped the US track down and kill Al Qaeda leader Osama bin Laden, who was sheltering in Pakistan.
After Trump's election, Islamabad's foreign policy chief Sartaj Aziz said his country was willing to work with him in fighting terrorism.
(Arul Louis can be reached at firstname.lastname@example.org)
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)