Modi "underlined his concerns on terrorism and expressed the hope that Pakistan will abide by its commitment to not allow its territory or territories controlled by it to be used for terrorist activities against India", Foreign Secretary Sujatha Singh told the media.
Modi called for a speedy trial of the Pakistanis accused of masterminding the Mumbai terror attack of 2008.
"The meeting was very constructive. Both sides were trying to address each other's concerns," she said.
"We want peaceful relations with Pakistan but for such relations to proceed terror should be brought to an end," Singh said when asked whether the meeting could open a new chapter in bilateral relations.
Asked if Modi raised the issue of underworld don Dawood Ibrahim who is said to be living in Pakistan, Singh refused to go into details on the 45-minute meeting between the two prime ministers.
"I don't want to go into details. It was a confidential meeting. Much more was discussed besides terror."
On Kashmir, she said that foreign secretaries of the two countries will meet and discuss the way forward. "Our stand on Kashmir is well known. We need not reiterate them."
She said Modi has been invited to Pakistan.