Modi also informed Trump that while India has the world's second-largest number of muslims, there were "considerably lower level" of Indian Muslims involved in or being radicalized in worldwide terror operations.
Trump previously supported India on Pakistan-sponsored terror, saying Modi would "take care" of the problem while answering reporters ' questions before they sat down for the bilateral.
"PM made it clear that that India is ready to talk with Pakistan, but for that it expects Islamabad to take some concrete measures which has not happened," Foreign Secretary Vijay Gokhale told journalists later.
Modi discussed in detail the challenges experienced by India, particularly in Jammu and Kashmir, due to terrorism.
"The PM pointed out that 42,000 lives have been lost as a result of terrorist attacks over the past 30 years and that it is the responsibility of the international community to join forces to fight the scourge".
India, however, expects the "overtures that PM made over the years and should have been reciprocated have never been reciprocated," he said, referring to Modi's visit to Lahore in December 2015 "with minimum protection." Shortly followed the terror attack on the Pathankot air base, and the attackers have not been brought to justice, Gokhale said.
"The focus of this time's debates was on the effect of terrorism and the fact that it needs to be understood where it's originating and how we deal with it together," he added.
On Trump's mediation offer, which he made again during Monday's press conference with Pakistan's PM Imran Khan, Gokhale said India's stance on the problem is quite evident that "if there are problems to be discussed with Pakistan, they will be discussed bilaterally."
( With inputs from IANS )