Speaking at the US Institute of Peace, a Washington-based think-tank, Asif said the "relationship with India is at the lowest ebb at the moment".
The minister claimed that a number of terrorist attacks in Pakistan in recent months had been traced back to elements operating from bases in Afghanistan.
Asif said that United States could not succeed in Afghanistan by waging war since USA troops were fighting the insurgents for the last 16 years.
Ahead of Tillerson's meeting with Asif, it was revealed that the Trump administration is concerned over the state of affairs in Pakistan, including its "subversive" role in the region, its issues with India and reports of a growing rift within the country between its military and civilian leadership. He insisted Pakistan has wiped out militant hideouts on its soil with little help from the USA, which has restricted military assistance to Pakistan, and it can't be blamed for the violence in Afghanistan. "India is threatening a limited war which could be unsafe for the regional peace", said a Pakistani official. "We are not saying that we are saints".
The minister urged the USA to take note of the gross human rights violations being perpetrated by Indian security forces in held Kashmir. "But since the last three, four years, we are wholeheartedly, single mindedly, we are targeting these terrorists", Asif said.
Asif, during his meeting with Tillerson at the State Department, defended Pakistan's role in the war against terrorism. He did not elaborate on what those steps might be.
Later, senior U.S. officials told various media outlets that the United States could stop providing economic and military assistance to Pakistan, degrade its status of a major non-Nato ally and place Pakistani officials with alleged ties to terrorists on a terrorist-watch list.
The diplomatic offensive unfurled by Pakistan to seek support of the regional countries including China, Russia, Iran and Turkey further solidified and strengthened Pakistan's position on the issue, which was amply manifested in the speech by the Prime Minister Shahid Khan Abbassi.
Pakistan can have strong economic benefits from India if it finds a way to carry out its global responsibilities and brings an end to any kind of terror safe havens on its soil, a top USA official told lawmakers. If that happens, nobody should expect restraint from us. "Pakistan believes that unless there is stability in Afghanistan, the dividends of peace in the region would continue to elude us".
Calling Gen Dunford's statement "baseless", he said Pakistan has acted against terrorists indiscriminately.