The US would like to see India and Pakistan have a "constructive conversation" leading to better relations, but that would depend on Islamabad cracking down on terrorism, according to a top US diplomat for South Asia.
The Acting Assistant Secretary for South and Central Asian Affairs, Alice Wells, said on Thursday that the conditions for talks between the nuclear-armed neighbours hinges on "Pakistan's seriousness of effort in ensuring that groups don't take advantage and engage in cross-border infiltration, that there are serious steps to implement the Financial Action Task Force action plan that Pakistan has committed to, and which includes the prosecution of UN-designated terrorists."
"So whether it's Hafiz Saeed who currently is in custody and under prosecution, but also chief of Jaish-e-Mohammed (JeM) Masood Azhar, who for long have been able to exploit their presence on Pakistani soil," it has to take action, she added.
Pakistan Prime Minister Imran Khan "has been very explicit that that is his intention and his objective" to take these steps, Ms Wells said.
If that happens, "can we then see a reduction in tensions between the two countries and productive engagement between the two?"
She said that President Donald Trump "has a strong relationship with the leaders of both India and Pakistan, and the world would benefit from reduced tensions and increased dialogue between the two countries. And given these factors, the President is willing to mediate if asked by both parties".
About Imran Khan's "strong statements", she said: "I would say in general across the region, a lowering of rhetoric would be welcome, particularly between two nuclear powers."
During her media briefing on the US diplomacy during the UN General Assembly session, she spoke on the situation in Kashmir.
"The US is concerned by widespread detentions, including those of politicians and business leaders, and the restrictions on the residents of Jammu and Kashmir. We look forward to the Indian government's resumption of political engagement with local leaders and the scheduling of the promised elections at the earliest opportunity," she said.
"As President Trump emphasised, Prime Minister (Narendra) Modi made a commitment that the recent changes to the status of Kashmir will improve the lives of the Kashmiri people, and we look to him to uphold this promise," she said.
Ms Wells said that members of Congress have raised the restrictions in Kashmir in letters to the administration. She added that "friends of India" want to see the nation move forward in ensuring human rights.
India-US ties were strong, she said referring to India's participation with the US, Australia and Japan in the Quad.
"The US and Indian joint participation in the Quad also demonstrates the strength of the US-India relationship and our shared commitment to, again, advancing a values-based policy towards the region," she said.
The Quad held its first ministerial level meeting in New York on Thursday.
Ms Wells said that trade is an important matter for Donald Trump and he spoke about reciprocity and fairness in trade during his General Assembly speech.
The US was making strides in reducing the trade deficit with India, with which "we enjoy a robust trade relationship with India, totalling $142 billion in trade in goods and services last year", she said.
Ms Wells attributed the reduction in trade deficits largely to increased energy exports.
She said the signing of a major memorandum of understanding between India's Petronet LNG and the Texas-based Tellurian for up to $2.5 billion in equity investment plus long-term liquid natural gas trade would translate to about 50,000 jobs and $60 billion in trade over the longer term.
"Talks on US market access are ongoing, and although we're not able to make an announcement this week, I'm confident that we are going to make progress on a trade deal," Ms Wells said.
Answering a reporter's question about human rights situation in Kashmir, Ms Wells said: "I would like to see the same level of concern expressed also about Muslims who are being detained in Western China, literally in concentration-like conditions."
"Being concerned about the human rights of Muslims does extend more broadly than just Kashmir, and you've seen the administration very involved here during the UN General Assembly and trying to shine a light on the horrific conditions that continue to exist for Muslims throughout China."
She did not directly mention Imran Khan, who has refused to publicly criticise the treatment of Muslims in China.