Indian Foreign Secretary Nirupama Rao raised the issue of terrorism during her three-hour meeting with her Pakistani counterpart Salman Bashir in New Delhi.
"It is the duty of Pakistan to dismantle terror infrastructure targeted against India," Rao told reporters after the meeting.
Rao confirmed that she had handed over three dossiers for Pakistan's attention, one on “individuals associated with Mumbai terror attack”.
She is understood to have called for firm action against the man suspected to have masterminded the Mumbai attacks, Hafiz Saeed, who is head of the banned Islamist group Lashkar-e-Taiba (LeT).
The second of India's dossiers concerned Ilyas Kashmiri, the commander of the Harkat-ul-Jihad al-Islami group that has threatened to attack upcoming sporting events in India.
The last dossier related to fugitive Indian nationals who are believed to be in Pakistan.
"We had set out to take a first step towards rebuilding trust and I believe my meeting with the Pakistan Foreign Secretary constituted that first step," said Rao.
"We have agreed to remain in touch," she added.
"It appears that both sides made a breakthrough in the sense that they're keeping future negotiations open," Mariana Babbar, diplomatic editor of The News in Islamabad, told RFI.
She expects Pakistan and India's foreign ministers to meet within the next month, while she says that the two countries' prime ministers could meet on the sidelines of the South Asian Association for Regional Cooperation (SAARC) summit in April.
The resumption of India-Pakistan dialogue has been welcomed by other world powers, including China and the United States.
But India's Hindu nationalist BJP party described Thursday's talks as "shameful" and "meaningless".
"Pakistan is supporting terrorists. It does not stop cross-border terrorism. It does not have control over terrorists moving freely in that country," BJP president Nitin Gadkari told a rally in New Delhi.
"I don't understand why we are holding talks with Pakistan's government when the people of that country do not listen to its government."
The official talks between Pakistan and India began in 2004, but were suspended following the Mumbai attacks in November 2008.