"Our focus with Pakistan is to enhance their capability and to deal with terrorist threats on their soil. They are fighting a serious and sustained campaign against violent extremism," White House Deputy spokesperson Mark Toner said.
"We do believe that they are making progress and taking steps to counter terrorist violence, but at the same time we have been very clear that they need to target all militant groups, including those that target Pakistan's neighbours, and close all safe havens," he said.
Diplomatic tensions between India and Pakistan have been rising since the September 18 attack on an army base in Uri in Jammu and Kashmir that killed 18 Indian soldiers.
Pakistan has rejected allegations of its involvement in the assault with both countries hitting out at each other including at the UN General Assembly.
Toner reiterated that it is the longstanding American position that the US believes India and Pakistan really stand to benefit from the normalisation of relations.
"We encourage both India and Pakistan to pursue and engage in direct dialogue that is aimed at reducing tensions," he said.
"We have long said that with regard to Pakistan, with regard to India, with regard to the region, there is no zero-sum game here. We are pursuing very close relations with India," the deputy spokesperson said.
"We have a deep and broad bilateral relationship and multilateral relationship, or work our multilateral issues with India. They are the world's largest democracy and we share a very similar vision of the world. And we obviously have very close trade and economic ties with India, and also that extends to security cooperation," he said.
"Similarly, we want to see Pakistan better able to respond to the threat that terrorism poses and terrorist groups that seek refuge in its territory," Toner added.
Swaraj in her address at the UN on Monday said there are nations "in our midst" where UN designated terrorists roam freely and deliver "their poisonous sermons of hate with impunity", an apparent reference to Mumbai attack mastermind and Jamaat-ud-Dawa chief Hafiz Saeed.
She also made a strong pitch for isolating such nations who speak the language of terrorism and for whom sheltering terrorists has become "their calling card".
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