The US has intensified its efforts in the past few months, including holding talks with the Taliban, to end the more than 17-year conflict in Afghanistan.
In the meeting with Khalilzad, Gokhale conveyed that India's preference is for having an elected government in Kabul and not an interim arrangement when the US withdraws its forces from the war-ravaged country, the sources said.
Khalilzad informed Gokhale about the issues under discussions with the Taliban and that Washington was insisting on an assurance that territory of Afghanistan will not be used for any terror activities.
India has been a key stakeholder in the peace and reconciliation process in Afghanistan.
In a significant move, India had sent two former diplomats in "non official" capacity to a conference on the Afghan peace process in Moscow in November last year which was attended by a high-level Taliban delegation.
India has been maintaining a policy of not engaging with the Taliban and pressing for an Afghan-owned and Afghan-led peace initiative to bring peace and stability in the war-ravaged country.
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