Mr Tillerson said he has asked the Pakistani leadership to take action against terror groups and an enhancement in their capabilities may pose a threat to the government in Islamabad.
"Terror havens will not be tolerated," Mr Tillerson said at a joint press conference with Ms Swaraj.
Ms Swaraj said Pakistan must dismantle terror infrastructure, insisting that any country backing terror groups must be held accountable. A host of issues, including ways to further boost defence and security cooperation and ramp up trade ties, were between Ms Swaraj and Mr Tillerson.
The US Secretary of State said the Trump administration was ready to share its best technology for India's military modernisation, adding that it looked forward to discussing deals for F-16 and F-18 fighter jets with New Delhi.
He said India was crucial to US-Afghanistan strategy and his government was looking at strengthening cooperation with India in the Indo-Pacific region.
Ms Swaraj said she raised the issue of H-1B visa with him and requested Mr Tillerson not to take action that might adversely affect Indians.