Ms Swaraj made her statement in both Houses on Monday.
With India and Pakistan agreeing to resume dialogue, Foreign Minister Sushma Swaraj told Parliament on Monday, "Whenever we talk, it is based on trust."
Ms Swaraj was replying to lawmakers in the Lok Sabha who wanted to know if India can trust Pakistan again. "When we have decided there will be no third party mediation, we will need to talk to each other," she said.
She said that "continued estrangement" between the two sides has been hampering peace and prosperity in the region, which is a shared vision of the two countries.
Pakistan has assured India it will expedite the Mumbai terror attacks case, she said in both Houses. The case is being heard in anti-terrorism court in Islamabad. A number of Lok Sabha members had also asked the minister to clarify on terrorism.
Her visit to Islamabad last week, she said, will be followed by 'Comprehensive Bilateral Dialogue' with Pakistan. The process will explore cooperation in trade and connectivity, people-to-people exchanges and humanitarian issues. "The new Dialogue, we sincerely hope, marks a new beginning also for peace and development in the whole region," she said.
Ms Swaraj's statement in the Rajya Sabha, on her visit, was drowned by protests led by the Congress in the Upper House. Ms Swaraj said Prime Minister Narendra Modi had discussed re-engagement with Pakistan with his counterpart Nawaz Sharif in Paris, leading to her visit. The two leaders had met on November 30 on the sides lines of the Climate change conference.
She later spoke in the Lok Sabha where lawmakers from 12 different parties asked questions about the visit and India-Pakistan ties. Ms Swaraj said, in her talks with Mr Sharif and Pakistan Foreign Minister Sartaj Aziz in Islamabad, the "two sides condemned terrorism and resolved to cooperate to eliminate this menace."
In the Lok Sabha, Ms Swaraj praised PM Modi. "He had started the process (of engagement with Pakistan) when he was PM designate by inviting SAARC leaders for the oath taking," she said.
The National Security Advisors of the two sides had met in Bangkok on December 6 and discussed "peace and security, terrorism, tranquility along the Line of Control and Jammu and Kashmir."